Here is the full list of all 38 Sonic Superstars achievements.
Cleared an ACT "Fruit".
Defeated the true boss.
Cleared Trip's story.
Cleared all of EGG FORTRESS.
Cleared all of FROZEN BASE.
Cleared all of CYBER STATION.
Cleared all of GOLDEN CAPITAL.
Turned super using the 7 Chaos Emeralds.
Cleared all of PRESS FACTORY.
Used the Goal Plate to reveal the hidden Item Box.
Used the White Emerald power "Extra".
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".
Used the Light Blue Emerald power "Water".
Collected 200 or more Rings when clearing a Stage.
Cleared all of PINBALL CARNIVAL.
Cleared a Stage with a friend.
Used the Purple Emerald power "Vision".
Cleared all of SKY TEMPLE.
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".
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.
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.