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