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