Full list of all 12 Sonic & Knuckles achievements worth 200 gamerscore. It takes around 4-5 hours to unlock all of the achievements on Xbox 360.
You completed the game as Knuckles.
You completed the game as Sonic.
You finished the Lava Reef Zone.
You finished the Sandopolis Zone.
You finished the Flying Battery Zone.
You collected all seven Chaos Emeralds.
You collected 100 rings.
You collected a Chaos Emerald.
You earned a Continue.
You started the game once with each character.
You entered a Bonus or Special Stage.
You finished the Mushroom Hill Zone.