Here is the full list of all 32 Boss 101 achievements.
Press the Do Not Press Button
First time on kite hill
Listen to the first tutorial
Complete Boss 101's main story
Pass Level 10 and Jolly Rog3r
Pass Level 20 and Back Track
Pass Level 30 and Mobius One
Pass Level 31 and Boss 101
Every boss piece defeated
Beat your first boss
Listen to all kite hill dialog
All gophers returned
Played one round of Endless Boss
Complete weapon collection
Complete hat collection
Dolphin partnership award
Top Local Score on Tank War
Top Local Score on Breakdown
Top Local Score on Mazard
Adopt all the pets
Beat every level in record time
Listened to all BERL's tutorials
Every Upgrade Complete
Receive first visitor
Receive all visitors
Press the Do Not Press Button Seven Times
Finish all hat quests
Purchase all Level 3 Guns
Pick Buzz Rainbow as a Pet Friend
Visit Gopher City for the first time
Get to level 20 in Endless Boss Arcade Mode
Get to level 20 in Endless Boss Iron Bot Mode