There is no way to make it correctly/correct.
It must be correctly, right?
Thanks!
No, it should be correct
It needs an adjective because in this context 'correct' is describing the pronoun (it) not the verb.
I always mix it up. Thanks!
I would say (as usual) that context is important.
1. Let's say you are trying to put together a piece of furniture which you bought in pieces but you have to build it yourself at home. You have been trying to do it for several hours but even though you are following the instructions carefully, you haven't been able to build it so that it looks how it should. You might say "Oh, this is ridiculous. There is no way to make it correctly!" Here, "it" would mean the "piece of furniture". However, I would say that we would be much more likely to use "put it together" or "build" than "make".
2. You are given an English exercise to do. You are told that a sentence is incorrect and that you need to change something (a word, punctuation) in order to correct it. You have tried everything you can think of but still your answer is wrong. You might say "It's impossible. There's no way to make it correct." Here "it" refers to "the sentence".
Personally, I would not use "make it correctly". In most cases, I think "do it correctly" would probably be the phrase you are looking for.