Going Under

Make sure to never miss an opportuninty of conversation with Ray. When the Dialog bubble is blue, he assigns you a task for mentorship:

Task one: Complete a job with 5 stars.
Easy to do in Joblin, just deal with goblins quickly.

Task two: Defeat 10 monsters with only your bare hands.
Not just finishing blow, also best done in Joblin.

Task three: Break up the Joblin Union.
A challenge room will show up in the Joblin dungeon and will have a task icon on the door.

Task four: Complete a floor without dodge rolling.
Just do not press A first floor in Joblin.

Task five: Acquire 10 skills in one run.
There are various ways of acquiring skills in a run, and it shouldn't be too hard to get ten skills:
Skill room, store, completing a floor, curse room.

Task six: Defeat the King Slime in Winkydink.
Another challenge room.

Task seven: Finish an end floor combat without taking damage.
Youtubed app helps, so do jobllin helpers that joined you. Then dodge. It can be done on any floor in the room with the exit slide.

Task eight: Reach floor B4 with no skills.
Unpin your skill before entering the dungeon. I found Joblin the easiest.

I found it easier to complete all these tasks before entering the rainbow dimensional portal in the middle for the "F" achievement. The dungeons get more difficult then.