Going Under

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

Task one: Deal 30 damage with explosives.
In Joblin Bean bombs and Sus boxes deal explosive damage. In Styxcoin the dynamite can be picked and thrown.

Task two: Apply status effects to 10 enemies
Easy status effects are frozen or on fire. Winkidink is a good place to get it done. By having Fern as your mentor you will come across fizzle cans instead of apps, which also helps toward the goal.

Task three: Toast a Jobwich.
You need to receive a jobwitch (consumable) in a room with fire, or bring a torch all the time. You must get the fire to the jobwitch, as you cannot pick jobwitch.

Task four: Defeat 3 Joblin Canbassadors with bean bombs.
Canbassadors are the goblins throwing them. Either grab dropped bean bomb can or make them fall on exploding one.

Task five: Find the Golden Eggplant in Winkydink.
Keep your eyes open in Winkidink and throw something at the yellow colored "low hanging fruit" to grab this.

Task six: Defeat a monster with a frozen monster.
Fire extinguishers freeze enemies and there are plenty in Winkidink. Pick frozen bodu with Y and bash nearest enemy.

Task seven: Have 9 Heart Containers.
You can get an extra heart container if you equip the Room for Growth skill. Ketchup bottles in stores add containers. Each of 3 defeated bosses makes you one heart container richer.

Task eight: Find the Fizzle Rock in Styxcoin.
You should always break rocks in Styxcoin, just for the crypto currency they yield. This one is red in color.

I found the task easy to do before entering the rainbow dimensional portal in the middle for the "F" achievement. The dungeons get more difficult then.