Seeing the Mad Doctor flying toward him with the intent to kill, Daneel activated the Basilisk's Breath right away.
His objective here was simple: he needed to put up a fight, and then survive.
Normally, others would have wanted to get this phase over with as quickly as possible. They would have just put up a token of a fight, and then ended the whole matter, as a Peak Warrior was not supposed to be able to put up any sort of a fight against an Exalted Champion, anyway. After all, why would one want to put themselves through more pain than was needed?
Of course, Daneel saw it differently. He knew the value of pain, in that it allowed one to go farther than they could even imagine. He knew the value of such an opportunity, where he could give it his all without thinking too much. He had an out which would definitely work, so he could choose to go with it if it got too dangerous.
But before that, he would not allow the Mad Doctor to get the satisfaction of crushing him.