Here is the full list of all 22 Chippy achievements.
The base game contains 21 achievements, and there is 1 DLC pack containing 1 achievements.
Complete Kraken without popping a single bubble
Complete Monarch stage
Complete Goliath stage
Complete Hermit stage
Complete Medusa stage
Complete Phobia stage
Complete Anomaly stage
Complete Overgrowth stage
Complete Execution stage
Complete Guardian stage
Complete Kraken stage
Complete Neophyte stage
Complete Prospector stage
Complete Storm stage
Complete Xulgon stage
Complete Neophyte with secret curse active
Complete Execution without shooting
Complete Overgrowth with at least +50 damage
Complete Medusa with bullet spawner powerup active
Complete Hermit without getting any powerups
Complete Xulgon after destroying each type of minion
Complete the Nightmare Invasion campaign