Lost game data when getting new phone, achievements etc

App data is stored in only two places, on your phone and as part of the iPhone backup. Restoring from backup, followed by syncing your iTunes content to your phone would have preserved your game data. Sounds like you set your new phone up as a "new" phone rather than restoring from the backup of your previous phone. Is that correct, and if so, do you want to fix things? If you do, it will require wiping your current phone.

The restore from backup process is all or nothing. There is no way to selectively restore data. If you want to restore the game data from your previous phone, you will have to first erase your phone and delete the current backup for your new phone. In essence, you'll be starting from scratch. You'll then be able to restore your backup from your old phone to your new phone.

You're welcome.

If you want to go that route, post back & I'll give you instructions.