Here is the full list of all 12 Chicken with Chainguns achievements.
Get "Rage Chicken" Power-up
Reach 10 kill streak
Collect 7 Sacred Hearts
Collect 2 ammo belts
Save 100 Chik'n Scratch
Get 20 Rubies in inventory
Get 10 Sapphires in inventory
Get 5 Emeralds in inventory
Kill 50 Baddies
Kill 100 Baddies
Kill 150 Baddies
Defeat the Big Bad Fox