Can I delete some game and earn all the trophies again?

If you haven't yet synced those trophies yet, then back up all your saves (to be safe), screenshots, anything else you care about, then delete your profile from your PS4. Once that process is through, add your profile back. You will lose any and all unsynced trophies, and can earn them again.

If you have already synced that game's trophies, you can add a new profile to your PS4 and play through the game again on that new profile, but they won't count towards your main profile.