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