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