As I might

Could this below be a grammatically correct answer?

A: How hard have you tried?
B: As I might.


No, it doesn’t sound right.

I have tried as I might (could).

or what could be the answer?


You may mean:

“I’ve / I have tried as hard as I can.”
“I tried as hard as I could.”

In response to “How hard have you tried?”, the former can be abbreviated to “As hard as I can”.

You may also be getting mixed up with the expression “to try with all one’s might” (e.g. “I tried with all my might”). This is not a very conversational expression in modern English; it’s more literary. Here, “might” is a noun meaning “power” (it’s a different word from the “might” in “I might watch a movie”, for example).