Here is the full list of all 47 Sonic Colors: Ultimate achievements.
Complete Planet Wisp
Get an "S" Rank on Any Act
Collect All 5 Red Star Rings in Any Level
Collect 300 Rings in One Run
Score 100,00 Points In One Run Using Quick Step
Complete Starlight Carnival
Destroy 100 Enemies Using Sweet Spot Homing Attacks
Complete Sweet Mountain
Set a personal best, and then break all of the numbers on the Results screen
Complete Tropical Resort
Get an "A" Rank on Any Act
Destroy 100 Enemies Using Homing Attacks
Beat A Previous Personal Best On Any Level
Destroy 50 Enemies Using Homing Attacks
Unlock All Achievements
Complete Aquarium Park
Complete Asteroid Coaster
Complete Terminal Velocity
Collect All 180 Red Star Rings
Collect the Green Chaos Emerald
Collect the Yellow Chaos Emerald
Collect the Silver Chaos Emerald
Collect the Red Chaos Emerald
Collect the Purple Chaos Emerald
Collect the Blue Chaos Emerald
Collect the Cyan Chaos Emerald
Finish Any Act As Super Sonic
Grab All 5 Red Star Rings in One Run on Any Act
Complete Any Act Without Picking Up Any Rings
Get 100% in Tropical Resort
Get 100% in Sweet Mountain
Get 100% in Starlight Carnival
Get 100% in Planet Wisp
Get 100% in Aquarium Park
Get 100% in Asteroid Coaster
Get 100% in Terminal Velocity
Complete Challenge Mode
Defeat Rotatatron With Less Than 3 Hits
Defeat Captain Jelly With Less Than 3 Hits
Get an "S" Rank Against Frigate Orcan
Defeat Refreshinator With Less Than 3 Hits
Defeat Admiral Jelly With Less Than 3 Hits
Get an "S" Rank Against Frigate Skullian
Get an "S" Rank Against Nega-Wisp Armor
Break Every Rank From D to S on the Results Screen
Collect all 30 Red Star Rings From Any Area
Play Through the Credits Level