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