Not sure if all-out can be used in this meaning
I will give all-out of me. Such as I will try to do the best of me?
"I will give all-out of me" is not a natural construction. There are two idioms you seem to be combining here: one is to go all out, and the other is to give something your all. They both mean that you'll try your hardest or best.
So a more natural version could be
"I will go all out [to do x]"
"I will give [the task] my all"
"I will give my all [to do(ing) x]"