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