Sorry if this has been posted, but I haven't seen it.
There is a cinematic at the very beginning of the Diablo fight, which I'm sure all of you have seen, where Diablo is suspended above the ground in a black aura. If the cinematic is skipped at the beginning then the aura breaks, Diablo falls to the ground, and the fight begins.
On the other hand, if you wait until after Diablo is on the ground to skip the cinematic then he does a roar/stomp animation, giving you some time to attack him before he attacks you.
The best time I have found to skip the cinematic is the moment the black aura breaks (before he lands on the ground). This causes the camera to shift back to your character while Diablo is falling to the ground and gives your control back before Diablo starts his roar/stomp animation, meaning you are free to damage him as much as possible without needing to dodge any attacks for several seconds.
It isn't a huge difference, but it's free damage and gets Phase 1 over with a little sooner.