Big BossG 25

This achievement will unlock after completing Ray's Mentorship. To do so, you have to finish 8 tasks given by him between dungeon runs (whenever Ray will have a blue bubble above him, it means you can get the next task), which are:

Task one: Complete a job with 5 stars.
The easiest way for doing this is in Joblin, sometimes you will walk into a room without enemies but with a floating 'J'. This 'J' is the job marker. Complete it by killing Joblins as fast as you can.

Task two: Defeat 10 monsters with only your bare hands.
As it says, kill 10 Joblins without a weapon (not even props).

Task three: Break up the Joblin Union.
After being assigned this task, sometimes you may spot a checkbox room. This means it's a room for one of the currently active tasks (either from Ray or any other mentor). The Joblin Union room will spawn only in the Joblin dungeon (duh) and it will contain a big number of Joblins. Kill them all to complete the task.

Task four: Complete a floor without dodge rolling.
Literally, just don't press the roll button on a single floor.

Task five: Acquire 10 skills in one run.
This should be quite easy to achieve, if you will consider the curse rooms and the shop skills. Otherwise, your best friend is getting one skill endorsed before a run and pinning it for the said run.

Task six: Defeat the King Slime in Winkydink.
Just like the Joblin Union, this will be in a checkmark room (on your minimap) but in Winkydink instead of Joblin.

Task seven: Finish an end floor combat without taking damage.
An end floor is a room with a slide to the next floor (not the boss floor, as you may have guessed). There will spawn about 5 enemies and likely you will get the Joblins either in a car or with burrito bombs, which will make a no-damage task quite hard. If you can, supply yourself in damage-increasing skills or in helpful apps.

Task eight: Reach floor B4 with no skills.
The B4 floor is the last and it is the boss fight floor. Unpin your skill (if you had one) and do NOT take any skills you may found during the run. On the safe side, I would also not recommend taking a curse.