This is an exageration, he has scenes throughout the movie where he has Two-Face style dialogue(in a similar style to the opening scene).
He's good in the scene where Carrey appears at his HQ.
He plays the robbery at Nygma Tech pretty straight when the scene opens, it's only when Batman appears that he gets excited and goes into clown mode.
He has the mix of dialogue and clowning again in the circus sequence, and is not too bad.
and plays it dead straight when he gets the drop on Robin.
I agree that he was pretty useless in the grand finale, but that was more Carrey's moment, he does get his own finale afterwards though.
In the scenes where he is ott cackling though, aye, it can be a bit too much, the scene where he is watching the secret id reveal for instance he goes into mugging overdrive, but the 'Say it..' 'You're a genius.' exchange at the end between him and Carrey was funny.
For the kind of Batman movie it is, a mix of serious and ott fun done in the colourful style of the 50s comics(which was intentional according to Schumacher on the dvd extras), he was not as bad a Two-Face as folk make out.