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