Here is the full list of all 24 COMET STRIKE achievements.
Clear level 1-5
Clear level 2-5
Clear level 3-5
Clear level 4-5
Clear level 5-5
Finish a game in endless mode
Use 10 skills
Use 50 skills
Use 200 skills
Clear 100 lines
Clear 500 lines
Clear 1000 lines
Finish a game with hard mode on
Clear level 5-5 wihout using a skill
Unlock all skills
Charge 100 charge shots
Clear 25 Levels
Clear 50 Levels
Clear 100 Levels
Play 100 Games
Play 200 Games
Play 500 Games
Play 777 Games
Drop 50 blocks