Steel Cage Ball: Score 200 points in one single game. This is easiest if you start from level 1, so delete and reinstall the game if you have to.

Black Bumps Ball: Score 400 points over a single game. Can be over the span of multiple levels.

Striped Ball: Score 600 points in one single game. See above tips.

Two-tone Ball: Play 15 games total. Each single level counts as one game, so if you beat five levels in one run, that's counted as five games.

Cube: Play 25 total games. Same counting as above.

Star: Play in 50 total complete games. Even if you lose right away it counts as a game.

Squiggly Line: Pass five levels. Best to delete the game and start over again from level 1 to make this easy to get.

Soccer Ball: Pass 15 levels. Same tips as above.

Rugby Ball: Play Helix Jump two days in a row. If you want this one right away, play a game, then set your phone time ahead by a day, then play again.

Multi-sided fractal: Play Helix Jump 7 days in a row. Same tip as above.

Hexagon Rings: Unlock five different new skins/shapes total. If you don't unlock this right away when you do that, then play a game apiece with those shapes.