"His enormous efforts to acting" or "toward acting" are both awkward. First, make effort singular. Then we need a verb after enormous efforts, such as "puts." Even so, I would not agree that "the effort he puts toward acting" sounds completely natural, either.
The more common idiomatic phrase would be "efforts/care/effort put INTO something"
Such as "He puts so much effort into his schoolwork"
"She puts so much care into her penmanship"
"He puts a lot of care into everything he does"
You could also say "the enormous effort he puts toward/into improving his acting."