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