Here is the full list of all 67 Popmoji achievements.
The base game contains 42 achievements, and there is 1 DLC pack containing 25 achievements.
Survive 30 seconds on Out Of Control
Survive 1 minute on Out Of Control
Survive 5 minutes on Out Of Control
Beat the game on Out Of Control
Beat the game on Moon Bouncer
Beat the game on Seasick
Beat the game on Rush Hour
Beat the game on Speedster
Lose on Speedster without ever dropping an emoji yourself.
Beat the game on Extreme Gravity
Beat the game on Original
Beat the game on One Shot
Beat the game on Shuffle
Survive 10 seconds on Keepie Uppie
Survive 30 seconds on Keepie Uppie
Survive 1 minute on Keepie Uppie
Survive 3 minutes on Keepie Uppie
Remove all emoji types at once with the Hammer ability
Switch 2 of the same emojis with the Shuffle ability
Squish an emoji
Squish 100 emojis
Squish 500 emojis
Drop an emoji outside of the box
Burn 5 or more of the same emojis at once
Use the Poof ability with only 1 emoji in the box