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