If you didn't know, there's an exploit (maybe once you reach Inferno).
I don't know if this works before you reach that difficulty, but you can try and then report back here.
This will skip many acts/quests and bring you right to the Prime Evil fight.
Go to Normal Mode or any other mode below your own.
Click Change Quest, scroll down to Prime Evil and select the last quest in the quest chain.
Then click "Join Public Game", and it should land you on the same quest, but on the hardest available difficulty.
If you wanted to join a random party and boost people through Diablo's fight (without party invites/friends), you can still do this by selecting the quest, joining, and then open it to public. But if you do this the other way, then you have the exploit.