InstitutionalizedG 10

After completing the first 10 levels with Bjorn (+ an additional trial level), you will have the option to go back and complete trials. This achievement is for completing all ten of these trials in the first segment of levels, Peggle Institute.

While everyone may have different ways of completing these, I've included some tips for each level that I found useful. Do with them what you will.

L1: Long and Long - Get 2 Long Shots
This one's pretty simple. You have two balls and therefore two opportunities to make two long shots. Take your time aiming your shot to hit a peg on one side and then a peg on the opposite side; do this twice. Remember that you can use cn_LB or cn_RB to add precision to your aim.

L2: The Skillz - Get 3 Free Ball Skillz Style Shots
A little more challenging than the first level, being as you have to time your shots to get into the bucket. There is no room for errors here; you are given one ball and are expected to make every single shot. Take your time lining up your shots to hit a single orange peg and then fall into the bucket. Bjorn's ability makes it pretty easy to line up your shots, but you'll need to learn through trial and error as far as making sure they land in the bucket.

L3: Duo-Slide - Get 2 Extreme Slides
Most of what I can tell you is already mentioned when viewing this level from the menu: "The super guide flares when you've got one lined up!" Aim your shots to either of pegs above the "C" shaped line of bricks. The bounce off of that peg will help line your shot up to slide down the bricks below it. When your super guide looks foresees the slide, fire away. Do this twice.

L4: Ridiculoso - Clear all the pegs.
Similar to L3. Line up your shot to the bottom lip of the "C" shaped set of bricks on the very top right. When you see that it'll slide around the inside of that first set of bricks, shoot. Luck may come into play here; it took me a few shots for it to wrap around properly and actually hit every brick.

L5: Big Skillz - Get 3 Free Ball Skillz Style Shots
This one is identical to The Skillz (L2) in that you are expected to make each shot into the bucket after hitting the orange pegs. The unfortunate part is that you are no longer assisted by Bjorn. I recommend aiming for the pegs most centered and trying to barely nic it to add as little angle to your shot as possible.

L6: Wall-Off - Get 3 Off the Wall Shots
Definitely one of the easier of the few trials. Aim your "shooter" at the wall and attempt to bounce off of the wall into one of the oranges. Know that you can't get a "Wall Shot" unless the wall is the first thing your ball touches. (Great, now I have "Get Low" by Lil' John stuck in my head.)

L7: Five Oh - Clear 50 Orange Pegs
Finally a trial in which you can select your character! Hoorah. Pick whatever master you are most comfortable using and clear the orange bricks. I got it on my first try using Bjorn, but I'm sure there are easier masters to do it with. Not much I can really add to that.

L8: Ultraviolet - Score over 500,000 Points
I'm not gonna lie, I got this one on accident. While the goal sounds difficult(er), the level is littered with purple pegs and you get unlimited super guide. I removed all the orange pegs outside of the "O" set of bricks in the center, then lined up a shot to slide around those bricks in the center. While I wasn't completely aware that the last shot I made was going to clear the last orange bricks, but I was surprised that I banked like 640,000+ just on that last shot. So try your best to save that "O" set of bricks untouched until the end and then slide your way to victory.

L9: Down Low - Beat the level under 175,000 Points.
I'm not the biggest fan of the "get a low score" trials, simply because it's not always the easiest to play sloppy and still complete the level. Here's some things to remember:
a. Avoid the purple pegs. Especially near the end of the level.
b. It isn't a bad idea to try to save your last green peg for the end. This makes it easier to line up your final shot to go off of the last orange peg and where the "10,000 bucket" will appear at the end. (I hit the 100,000 bucket the first time I tried and failed the trial.)
c. While points awarded for extra balls at the end isn't super drastic, it isn't a bad idea to make sure you are almost out of balls before lining up your last shot.

L10: Target Practice - Hit all 4 fast-moving pegs.
This one took me a while. While I'm sure other players are significantly better at timing these shots, I couldn't hit a single orange peg the first time I tried. I adopted the habit of just shooting directly into the bucket every shot. If an orange peg got hit along the way, so much the better. This technique may take a while, but as far as getting started, the bucket was incredibly helpful to me.

After you've completed the last level, the achievement will pop and you'll be awarded another Bjorn costume.
Best of luck!