The challenges tab is in the campaign and is the one on the far right.

General hints:
1. The title is a clue on how to defeat the challenge.
2. You seem to have exactly enough mana to beat the challenge. Efficency is key.
3. A number of the latter challenges require unorthodox play. Think outside the box. Being able to abuse rules will help.

Reverse the Assault
Garruk will attack with everything. If you don't block efficiently you will die right now. Use the cards available to win on your next turn.

HINT: If a creature becomes blocked and it's blockers are removed before the damage step it will not deal damage to you. (Creatures with trample are exempt from this.) Firebreathing is essentially 1 Red Mana = 1 point of damage.

SOLUTION:
Let Garruk attack and block Sentinel Spider with Goblin Piker.
After blockers are declared, use Fling.
Now be careful. First TARGET Deadly Recluse then sacrifice Goblin Piker.
Play Mountain.
Use Act of Treason on Sentinel Spider then attack with everything.
Before damage, pump up Dragon Hatchling four times.

Exalted Army
You have a number of creatures while your opponent has a few flyers. Some of your creatures have exalted and other are unblockable. You must win this turn.

HINT: Exalted sucks. Pacifism is awesome.

SOLUTION:
Cast Pacifism on Rune-Scared Demon, and the other Pacifism on Lumenegrid Gargoyle.
Attack with everything.
Serra should block Nefarox, before damage cast Seize the Initiative on Syhunter Skirmisher.

Drake Expectations
Garruk is protected by his insane life total (42) and a ridicoulous amount of Giant Spiders (2/4 Reach). Using your spells namely Time Warp and Talrand's ability, win before Garruk gets a turn.

HINT: You have 7 mana. 3 Red, 4 Blue. Remember to tap carefully. Time Warp allows you an extra turn, which is essentially untap and draw a card. Sage Owl will allow you to see your next 4 cards. Plan ahead.

SOLUTION:
Cast Sage Owl.
Put the cards back in the following order: Blaze, Furnace of Wrath, Mountain, Time Warp. (Time Warp is on top)
Cast Time Warp targeting yourself and go to your next turn. Don't attack.
Cast Time Warp targeting yourself leaving two Mountains untapped, stop time (press X).
Respond by casting Reverberate targeting Time Warp on the stack.
Target yourself with the copied Time Warp.
Go to your next turn without attacking.
Play Mountain. Cast both Talrand's Invocation cards.
Go to your next turn without attacking.
Cast Furnace of Wrath leaving at least one Mountain untapped.
Cast Rupture. On resolution, sacrifice Talrand.
Attack with everything.

Stolen Goods
Talrand will cast Mind Control targeting your Cudgel Troll. Win this turn.

HINT: Mind Control will let Talrand control Cudgel Troll. While Cudgel Troll still has his equipment, remember that YOU still control the equipment. Talrand also has an active Pit Trap ready for use. You remembered the lesson from Reverse the Assault right?

SOLUTION:
Equip Leatherback Baloth with Lightning Greaves.
Equip Ring of Kalonia to Garruk's Packleader.
Equip Lightning Greaves to Garruk's Packleader.
Go to Combat and attack with Garruk's Packleader.
Let Talrand block with Cudgel Troll, and cast Divine Verdict on Cudgel Troll.

Obliterate This!
Phyrexian Obliterator is extremely annoying. Whenever it is dealt damage, YOU sacrifice one permanent for every one point of damage it took. You have two turns to win, Liliana won't do anything but attack with Gargoyle on her turn.

GLOSSARY: Undying: If a creature with Undying dies (goes to the graveyard from the battlefield) it comes back into with a +1/+1 counter, if it did not have any +1/+1 counter on it.

HINT: With Flayer of the Hatebound, when a creature of yours 'undies' it deals that much damage to target creature or player equal to it's new power.

SOLUTION:
Cast Cloudshift on War Priest of Thune.
Use its ability to destroy the Arrest on Flayer of the Hatebound.
Go into combat and attack with Flayer of the Hatebound.
Let Liliana block with Phyrexian Obliterator, stop time (press X).
Cast Seize the Initiative on Flayer of the Hatebound.
Respond to it by casting Undying Evil on Oxidda Scrapmelter. Let resolve.
Sacrifice the following due to Phyrexian Obliterator: Flayer of the Hatebound, Oxidda Scrapmelter, Swamp, Plains, Plains.
With Flayer of the Hatebound's trigger, deal damage to Liliana.
With Oxidda Scrapmelter's trigger, destroy Lumengrid Gargoyle.
With Flayer of the Hatebound's trigger, deal damage to LIliana.
Let the turn end.
Let Liliana's turn end.
Play Plains, attack with everything.

Say Your Praetors

You only need to beat this challenge once to move to the next one. There is an achievement for beating it five ways.

Praetors are legendary creatures which gives a bonus to its controller and a mirrored hinderence to the controllers opponents. Jace controlls ALL of them, one of every color. When you open the challenge it shows you the five colors. Each will crack once you complete the challenge by slaying that specific creature, and winning the challenge due to. It is Jace's turn and he will attack with everything. You must sucessfully defend with Baneslayer Angel. You must win on your turn (going after Jace).

PRAETORS:
Black: Sheoldred the Whispering One
At the beginning of its controllers upkeep, return target creature card from the graveyard to the battlefield.
At the beginning of an opponent upkeep, they sacrifice a creature.

Blue: Jin-Gitaxias, Core Augur
At the beginning of the controllers end step, draw seven cards.
Each opponents maximum hand size is reduced by seven.

Red: Urabrask the Hidden
Creatures the controller controls have Haste.
Creatures your opponents control enter the battlefield tapped.

Green: Vorinclex, Voice of Hunger
Whenever an opponent taps a land for mana, that land doesn't untap on the next untap step.
Whenever you tap a land for mana, add one mana to your mana pool of any type that land produced.

White: Elesh-Norn, Grand Cenobite
Opponents creatures have -2/-2
Other creatures the controller controls have +2/+2

As you can see some abilities don't matter.

HINTS:
Sheoldred:
Removing Sheoldred means that you keep Baneslayer Angel. Use her to attack. Jace will try to kill her, protect her. Jace is on 4 life.

Jin-Gitaxias:
Removing Jin-Gitaxias makes Jace not draw cards on his end step, therefore he doesn't attempt to Thought Scour (drop 2 cards from the top of your library) you. Use the cards you wouldn't have drawn otherwise. Jace is on 4 life.

Urabrask:
Removing Urabrask means that creatures won't come into play tapped. Jace is on 4 life. Evade Elesh-Norn.

Vorinclex:
Removing Vorinclex gives you more access to mana compared to all the others. Jace is on 4 life. Burn him.

Elesh-Norn:
Removing Elesh-Norn removes his only blocker on your turn while growing your creatures back to normal size. Jace is on 4 life. Use a creature to pound him.

SOLUTION:
Block whichever creature you want to kill with Baneslayer Angel, stop time and cast Brute Force on the Angel, and stop time again. Then do the following dependant on which creature you kill.

Sheoldred:
Cast Giant Growth on Baneslayer Angel.
Go to your turn.
Cast Sizzle, leave a Plains untapped.
When Jace attempts to kill Baneslayer with Leaf Arrow, respond with Veteran's Reflexes.

Jin-Gitaxias:
Keep going to your turn, sacrifice Baneslayer on your upkeep.
Cast Avatar of Might.
Cast Niveous Wisp's on Elesh-Norn.
Cast Burst of Speed.
Attack.

Urabrask:
Keep going to your turn, sacrifice Baneslayer on your upkeep.
Cast Avatar of Hope.
Cast Burst of Speed.
Attack, cast Giant Growth on Avatar of Hope before damage.

Vorinclex:
Cast Giant Growth on Baneslayer Angel.
Respond to Thought Scour with Parallectric Feedback, targeting Thought Scour.
Go to your turn, sacrifice Baneslayer on your upkeep.
Cast Sizzle.

Elesh-Norn:
Cast Giant Growth on Baneslayer Angel.
Go to your turn, sacrifice Baneslayer on your upkeep.
Cast Spark Elemental.
Cast Veteran's Reflexes on Spark Elemental.
Attack.

Desperate Measures
Yeva sits comfortably in the stalemate on 22 life and a tough army. Win this turn by beating through her.

HINTS: I'll reiterate a hint that the game gives. Having 1 life is fine, as long as your has opponent has 0. Both Death's Shadow and Faith's Shield work better if you're on low life.

SOLUTION:
Cast Phyrexian Processor.
On resolution pay 7 life.
Cast Earthquake paying 4 for X, make sure to leave 1 Plains untapped, stop time.
Attack with everything.
Respond by casting Faith's Shield on any permanent, on resolution say "blue".

Sculpting the Perfect Warrior
You have essentially been controlled out of the game thanks to an Arrested Purestel Paladin, and Teferi's Moat. Find a way to win this turn.

GLOSSARY: See that weird blue symbol on Phyrexian Metamorph? This is called Phyrexian Mana. Phyrexian Mana regardless of color can be paid with 2 life or whatever the color is. So to cast Phyrexian Metamorph you can pay 4 mana of which one must be blue OR 3 mana and 2 life. You cannot pay 2 life if you do not have at least 2 life, and paying 2 life when you have 2 life will lose the game immediately as you will have no life.

Living Weapon means that once the equipment enters the battlefield it becomes a equipped to a Black Germ token that is 0/0. Black creatures cannot attack Odric thanks to his Teferi's Moat.

HINT: This one is pretty headache inducing as you have to understand how some cards work. The most important are Scultping Steel, Mortarpod, Batterskull, and Phyrexian Metamorph.
Remember that you still have Metalcraft so the Paladin's Ability WILL trigger despite it not being able to attack.
Remember that Lifelink is ANY damage.
Take a good look at all the board.

SOLUTION:
Whenever I say Equip, always use the equip cost of 0. If the game asks if you would like to draw a card ALWAYS say yes. You cannot mill yourself to death, trust me, I've checked. Asteriks (*) show where you would be asked to draw cards.

Equip Batterskull to Germ token.
Sacrifice the Germ token to deal 1 damage to Porcelain Legionnaire.
Cast Sculpting Steel, on resolution copy Batterskull*.
Equip Mortarpod to Germ token.
Sacrifice the Germ token to deal 1 damage to Porcelain Legionnaire, it should now die.
Cast Phyrexian Metamorph, copy Paladin on resolution.
Cast Sword of Feast and Famine**.
Cast Darksteel Axe**.
Equip all the equipment possible to the copied Puresteel Paladin (the copied Puresteel Paladin will be artifact grey as opposed to pure white, and will have a copy icon on it just like the copied Batterskull)
Go into combat and attack with it.
Return the copied Batterskull to your hand, (Press RT on the copied Paladin, then find the copied Batterskull and return it)
Cast Sculpting Steel, on resolution copy Mortarpod**.
Play Island.
Cast Repulse targeting the Paladin enchanted with Arrest.
Cast Puresteel Paladin.
Sacrifice the Germ to deal 1 damage to Odric.
Sacrifice the copied Paladin to deal 1 damage to Odric.
Equip either Mortarpod to Paladin.
Sacrifice the Paladin to deal 1 damage to Odric.

Replica's Revolt
The HILLS ARE ALIVE, AND THEY HAVE EYES! All lands are 2/2 creatures as well thanks to Nature's Revolt. Find a way to kill Garruk on 6 life this turn. You have 26 Islands and Garruk has 24 Forests.

HINT: Don't bother trying to land outnumber him, there is no efficient way to do so. Lands still have summoning sickness, and cannot be tapped for mana if they are also a creature.

SOLUTION:
Cast Rite of Replication Kicked on Archaeomancer.
For the five triggers, return three Rite of Replication and any other two cards.
Cast Rite of Replication Kicked on any Forest.
Cast Rite of Replication on Ursapine.
Cast Rite of Replication on Acidic Slime, it is cruicial that you do this last.
With Acidic Slime's trigger, destroy Nature's Revolt.
Go into combat and attack with Archaeomancer, stop time.
Using Ursapine's ability, pump up the attacking Archaeomancer five times.

Goblin Raider's
NOTE: You may need to turn off Simplified Targeting in the options to be able to do this.

Ajani has you beat with three Baneslayer Angel's and 14 life. With the Angel's having First Strike and Lifelink, sneak your Goblin's past the Angels and kill Ajani.

HINT: If Baneslayer attempts to block a creature that is removed from combat, Baneslayer will not deal any damage. Therefore they wouldn't gain Ajani life.
There is some tricky combat math here, but trial and error will help understand it.
Notice Gut Shot's mana cost.

SOLUTION:
Cast Goblin Ringleader.
Tap Temple Bell.
Go into combat and attack with everything.
As soon as the Angels show what they're blocking, stop time.
Cast Chandra's Fury on yourself.
With Goblin Arsonist's trigger, deal 1 damage to either creature being blocked (a creature being block has a yellow arrow pointing to the creature blocking it), stop time.
Cast Gut Shot, targeting the last creature being blocked.

Credit to DomaDragoon for the solutions to the Praetors puzzle.