Hey Felbreak!
Once you've earned the achievement itself it's saved to your account, so you won't lose it if you delete the character you did it on. However, there really isn't a need to delete a character to start over with a friend unless you have no characterslots left on that realm. You might regret doing so later and while you can restore your own characters this does come with a cooldown, so please don't make that decision too quickly.