Here is the full list of all 36 Sonic Origins achievements.
Unlock all Trophies
Clear 10 Sonic the Hedgehog 2 Missions with an S rank
Clear 10 Sonic the Hedgehog 3 & Knuckles Missions with an S rank
Defeat 10 Rhinobots in Sonic the Hedgehog 3 & Knuckles
Clear 10 Sonic CD Missions with an S rank
Turn into Super Sonic
Defeat 10 Stingers in Sonic the Hedgehog 2
Defeat 10 Moto Bugs in Sonic the Hedgehog
Clear Sonic CD in either Anniversary or Classic Mode
Clear all 4 titles
Clear 10 Sonic the Hedgehog Missions with an S rank
Clear Sonic the Hedgehog 3 & Knuckles in either Anniversary or Classic Mode
Glide as Knuckles
Clear Sonic the Hedgehog 2 in either Anniversary or Classic Mode
Fly as Tails
Collect 3 types of Shields in Sonic the Hedgehog 3 & Knuckles
Unlock 30 art collection items with Coins
View a Premium Collection item from the Museum
Play Mirror Mode
Get the jackpot in Sonic the Hedgehog 2's Casino Night Zone
Unlock 10 sound collection items with Coins
Unlock 6 movie collection items with Coins
Try the Boss Rush from any of the titles
Win a race against Metal Sonic in Sonic CD
Travel to the past or future in Sonic CD
Watch the opening for Sonic CD
Watch the opening for Sonic the Hedgehog 3 & Knuckles
Defeat a total of 200 enemies
Clear 1 Mission
Watch the opening for Sonic the Hedgehog 2
Clear Sonic the Hedgehog in either Anniversary or Classic Mode
Collect a total of 1000 Rings
Defeat 30 enemies with the Spin Dash
Use Air Bubbles in Sonic the Hedgehog
Defeat a total of 50 enemies
Watch the opening for Sonic the Hedgehog