Here is the full list of all 31 Fly Punch Boom! achievements.
Unlock Lord Rekt
Unlock Bud
All stage kills in the two cities
All stage kills beyond the stars
All stage kills under the sea
All kills among the dunes
All stage kills in the sacred cave
All fatalities
Unlock all lore pages
Finish the tutorial
Beat Shin in the tutorial
Stare into all the eyes of joy
Share your heart with a friend
Do 3 teleport combos in 1 round
Beat arcade mode in hard difficulty
Charge special energy by taunting 10 times
Kill both opponents in 2v2 after your friend gets killed
Decapitate 10 times
Stop a special with another special
Counter a special with an object
Throw a big blob of cotton candy at your opponent
Play 100 rounds
Play 500 rounds
Play 1000 rounds
Play 100 online rounds
Finish arcade with all cosplays
Mash super fast in power clash
Avoid certain death x2 in 1 round
Do a 3 teleport combo
Decapitate with a mega uppercut
Do a combo with 3 objects