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