Here is the full list of all 21 Bomb Fight achievements.
Drop a bomb
Drop a red bomb
Reach maximum speed
Use fire skill
Use ice skill
Use electric skill
Use wind skill
Use black hole skill
Alternate time speed
Reach power 10 with your bomb
Reach power 50 with your bomb
Get 3 active skills at one
Get 4 active skills at one
Reach 100 rounds (in total)
Use a remote bomb
Find the test room
Play in FFA (3 rounds or more)
Play in Team (3 rounds or more)
Play in Score mode (5 kills or more)
Play in Color mode (3 rounds or more)
Explode 25 bombs at once