Welcome to Android Central! Look at the contacts on the phone that aren't syncing with your Google account, and make sure they're associated with the Google account, and not the local Phone account. You can find that by editing the contact and looking at one of the first fields, which should tell you which account they're in. If it's the local Phone account, those don't get synced with Google. I'm not sure if you can simply change the account for the contact--you may have to reenter the contact, this time selecting the Google account instead of the Phone account.