The following things will unlock these the achievements:
Score 500,000: Get 500,000 points
Score 1,000,000: Get 1,000,000 points
Pacifism: Survive the first 60 seconds of the game without firing or using a bomb
Multitastic: Get a 10x multiplier
Extra Bomb (Evolved): Get 100,000 Points
Extra Bomb (Retro): Get 25,000 Points Mad Cat Skills: Get 9 lives
Quatermaster: Get 9 bombs
Score 100,000: Get 100,000 points
Score 250,000: Get 250,000 points
Survive 100,000: Get 100,000 points without dying
Survive 250,000: Get 250,000 points without dying
Extra Life (Evolved): Get 75,000 Points
Extra Life (Retro): Get 20,000 Points
Survive 500,000: Get 500,000 points without dying
Survive 1,000,000: Get 1,000,000 points without dying