I know the above is NOT "Is an fear me" for several grammatical reasons.
Would the correct way be "Is mise an fear"?
I assume there's more than one way to say it.
Thanks in advance.

Yes.
Is mise an fear (normal)
Is mé an fear (not so often)
Is é an fear mé. (very rare: I am the (famous, special, prophesied) man. So rare, most grammars don't even mention it or exclude it explicitly.)

and
Tá mé ar an bhfear ... (but only if accompanied by a superlative, e.g. ... ar an bhfear is mó or an ordinal number , e,g. ... ar an chéad fhear a tháinig, etc.)