Here is the full list of all 33 Popplings achievements.
Completed your first battle
Completed a battle on Hard mode
Played a Battle locally with two players
You created a combo of two or more in Battle
You created a combo of five or more in Battle
You shot a popple with less than 1 second left on the pressure timer
You parried a popplings battle for more than five minutes in a single game
Completed Story Chapter 1
Completed Story Chapter 2
Completed Story Chapter 3
With a hat, buddy! Completed Story Chapter 4
Completed Story Chapter 5
Completed Story Chapter 6
Completed Story Chapter 7
Completed Story Chapter 8
Completed Story Chapter 9
Completed all puzzles in World 1
Completed all puzzles in World 2
Completed all puzzles in World 3
Completed all puzzles in World 4
Completed all puzzles in World 5
Completed all puzzles in World 6
Completed all puzzles in World 7
Completed all puzzles in World 8
Completed playing your first custom puzzle
Created your first ever custom puzzle
Playtested your puzzles at least ten times
Won your first Online Battle
Lost your first Online Battle
Won a Popplings battle in under 60 seconds
Saved over ten custom puzzles
You unlocked Extreme difficulty in Story mode
You completed Story mode on Extreme difficulty!