Here is the full list of all 20 Jump Stars achievements.
Entered into Tournament Mode
Entered into a custom gamemode with 1 game in the playlist
Entered into a custom gamemode with 9 games in the playlist
Punched 1,000 times overall in the game
Punched 5000 times overall in the game
Punched 10,000 times overall in the game
Jumped 1,000 times overall in the game
Jumped 5,000 times overall in the game.
Jumped 10,000 times overall in the game
Gained 25,000 teamscore overall in the game
Gained 50,000 teamscore overall in the game
Gained 100,000 teamscore overall in the game
Gained 250,000 teamscore overall in the game
Gained 1,000,000 teamscore overall in the game
Eaten 1,000 Pies in Collected overall in the game
Broken 1,000 barriers in Drop overall in the game
Achieved 3,000 teamscore in a mini-game in a single play
Completed Tournament (including Gauntlet) with 2 players
Completed Tournament (including Gauntlet) with 3 players
Completed Tournament (including Gauntlet) with 4 players