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