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