Here is the full list of all 15 Bomb Party achievements.
Finish editor tutorial
Win a game
Play 100 games
Play 300 games
Play 1000 games
Get 3 stars 10 times
Rate 10 levels
Upload 3 levels
Upload 10 levels
Destroy 10,000 cubes
Destroy 30,000 cubes
Destroy 100,000 cubes
Hit the player from a long distance
Hit the player who is still landing
Did not step on the floor and fall directly