Here is the full list of all 16 Centipede: Recharged achievements.
Reach 40 000 points in arcade mode
Kill 15 enemies in rapid succession
Reach 30 000 points in arcade mode
Survive 3 minutes
Reach 20 000 points in arcade mode
Kill the enemy without doing damage to it
Reach 2 000 points without missing a single shot.
Complete all challenges in a single player mode
Complete all challenges in coop mode
Resurrect an ally in coop mode
Kill 10 enemies with a single shot from a railgun
Detonate 50 bombs with a single shot
Kill 1000 centipedes
Kill 400 scorpions
Kill 600 fleas
Kill 800 spiders