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