INCORRECT: I've done what I should've been done. CORRECTION: I've done what should've been done. CORRECT: I've done what I should've done.

You can say - I've done what I should have. ( Meaning that you did the correct thing for you PERSONALLY. For example, you looked after your sick mother)) Or I've done what should have been done. ( Meaning you did what seemed the necessary, proper moral thing for anyone to do. For example, you returned a wallet you found on the street) Hope this helps

The first difference is that only the second sentence is grammatical. “I’ve done what should have been done” is grammatical, without a specific pronoun; here the prefect tense is a kind of passive, so that there is no subject for that part of the sentence — some action needed to be done by *someone*, and “I” did that action. If this is what you mean, it is okay. The second difference is that the second sentence has a clear focus on the speaker’s own actions.