It's not possible to claim all Achievements first time around, as finishing later Tiers will unlock new races in older Tiers. Try completing all of the initial races in all five Tiers; once you have done so, return to Tier 1 and you should find new races available.
This could also be caused by a known issue with Game Center, which can usually be fixed by fully closing the Game Center app, then reopening it.
To do so, please follow these steps:
- Return to the iOS home screen
- Double tap the Home button on your device. A menu should slide open at the bottom of the screen
- Press and hold the Game Center icon in this bottom menu
- After a second, a minus sign should appear at the top corner of the app icon.
- Tap the minus sign to fully close the app.
- Repeat steps 2-5 for our game.
- Reopen the app. It should load in correctly.