Here is the full list of all 34 Sonic's Ultimate Genesis Collection achievements worth 1,000 gamerscore.
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Sonic The Hedgehog: Obtain a Chaos Emerald
Dr. Robotnik's M.B.M.: Complete the game
Kid Chameleon: Collect Maniaxe
Play all Arcade Titles
VectorMan: Collect 500 photons
Super Thunder Blade: Score over 1,500,000 points in the first level
Streets of Rage 3: Unlock Roo the Kangaroo as a playable character
Play all Genesis™ Titles
Streets of Rage: Complete 1st Level using all 3 characters
Sonic 3: Collect 100 rings with Tails anywhere on Angel Island Zone
Sonic Spinball: Get 10,000,000 points in the first level
Sonic 3D Blast: Rescue 20 Flickies.
Ristar: Collect 5 Yellow Stars
VectorMan 2: Reach Scene 11
Comix Zone: Complete first episode
Fatal Labyrinth: Progress to the fifth level of the labyrinth
Golden Axe II: Complete Tower Level
Golden Axe III: Use magic 10 times
Golden Axe: Collect 20 magic power-ups
Flicky: Collect 80,000 points
E-SWAT: Obtain the Combat Suit (Complete Mission 2)
Decap Attack: Collect 5 Bonus Coins
Columns: Get 20,000 points only on Easy Mode
Alien Storm: Reach Mission 3 without losing a life
Beyond Oasis: Unlock the Water Spirit
Bonanza Brothers: Reach 40,000 points on the first level
Shinobi III: Complete first level without using continues
Altered Beast: Collect 100,000 pts or higher by the end of the first level
Ecco: The Tides of Time: Eat 200 fish
Ecco: Talk to another dolphin
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Alex Kidd: Collect 1,000 in currency