Here is the full list of all 44 Cubemen achievements.
Collect 50 Heal Bonuses
Collect 150 Bonuses
Play & Win all Defense Levels
Kill 50,000 Enemy Cubemen
Collect 50 Freeze Bonuses
Collect 50 Destroy Bonuses
Collect 100 Bonuses
Collect 20 Heal Bonuses
Collect 20 Freeze Bonuses
Collect 50 Bonuses
Collect 20 Destroy Bonuses
First time you earn a Bronze Medal
Buy 900 Cubemen
Buy 500 Cubemen
Earn 90,000 Cubes
Kill 10,000 Enemy Cubemen
Earn 50,000 Cubes
Kill 5,000 Enemy Cubemen
Earn 25,000 Cubes
Earn 10,000 Cubes
Kill 1,500 Enemy Cubemen
Collect 10 Bonuses
Earn 5,000 Cubes
First time you win a Team Mayhem game
Earn 5x Platinum Medals
First time you earn a 10x Multiplier
Buy 150 Cubemen
First time you win an Individual Mayhem game
First time you earn a Silver Medal
Earn 1,500 Cubes
First time you earn a 7x Multiplier
First time you win a Skirmish Game
Buy 50 Cubemen
Kill 250 Enemy Cubemen
First time you earn a Gold Medal
Earn 500 Cubes
First time you earn a 5x Multiplier
First time you win a Defense Game
First time you earn a Platinum Medal
Earn 150 Cubes
First time you earn a 4x Multiplier
Kill 25 Enemy Cubemen
Earn 50 Cubes
First time you earn a 2x Multiplier