Both expressions are valid English and yet they probably don't quite convey the meaning you intend. Here is a (slightly modified) extract of a discussion of acting:
for some, it is how perfectly an actor changes his accent, body
language & mannerisms in accordance to the demand of role etc.. I
personally find it really remarkable & commendable when an actor seems
natural on screen, as if he's totally unaware of the presence of
The key difference is that word natural is not applied to the acting but instead to the actor. As you have expressed it, there is an slight implication that no acting is actually taking place, the actor is just being his or her self. In fact they will be expressing a range of emotions in such a way that the audience forgets that they are acting.
A less important problem with your first phrase is that for many it will bring to mind an old song "Act Naturally", recorded by Buck Owens, The Beatles and others.
Well, I hope you come and see me in the movie
Then I'll know that you will plainly see
Biggest fool that's ever hit the big time
And all I gotta do is act naturally
We'll make the scene about a man that's sad and lonely
And begging down upon his bended knee
I'll play the part but I won't need rehearsing
All I have to do is act naturally
Well, I'll bet you I'm a gonna be a big star
Might win an Oscar, you can never tell
The movie's gonna make me a big star
'Cause I can play the part so well
Songwriters: MORRISON VONI / RUSSELL JOHN BRIGHT
Which indeed implies that there's no acting happening at all.