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