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