Here is the full list of all 38 Sonic Superstars achievements.
Used Sonic's Drop Dash to defeat 100 enemies.
Collected 10,000 Rings.
Defeated the true boss.
Cleared Trip's story.
Cleared a Stage with a friend.
Cleared all of EGG FORTRESS.
Cleared all of FROZEN BASE.
Cleared all of CYBER STATION.
Cleared all of GOLDEN CAPITAL.
Collected 200 or more Rings when clearing a Stage.
Turned super using the 7 Chaos Emeralds.
Cleared all of PRESS FACTORY.
Used the White Emerald power "Extra".
Used the Yellow Emerald power "Slow".
Used the Green Emerald power "Ivy".
Cleared all of SAND SANCTUARY.
Cleared all of LAGOON CITY.
Turned Lagoon City's Goal Plate into a pile of fruit.
Cleared all of PINBALL CARNIVAL.
Used the Light Blue Emerald power "Water".
Used the Goal Plate to reveal the hidden Item Box.
Cleared an ACT "Fruit".
Cleared all of SKY TEMPLE.
Used the Purple Emerald power "Vision".
Cleared all of SPEED JUNGLE.
Cleared 1 Bonus Stage.
Used the Red Emerald power "Bullet".
Cleared all of BRIDGE ISLAND.
Used the Blue Emerald power "Avatar".
Used Tails' aerial attack to defeat 100 enemies.
Used Knuckles' glide to defeat 100 enemies.
Used Amy's Hammer to defeat 100 enemies.
Used Trip's double jump to defeat 100 enemies.
Cleared Zap Scrap in Frozen Base without taking damage.
Collected 100 Medals from Bonus Stages.
Collected 600 or more Rings from ACT "Fruit".
Defeated 1,000 enemies.
Defeated the gold enemies in all Stages.