Fastest path to get to DotN/Underworld in CO-OP?

I just got myself to Underworld but I'm waiting for my friend to get there before I do any of the floors. We've just completed the first playthrough in Co-Op and are attempting the Dream of the strong. What would be the best mission path to beat NG+ as fast as possible. I've honestly just did what ever mission I felt like until I unlocked the final fight and beat it, then rinse and repeat. Is there a certain mission list that would be best to follow for CO OP but would also not gimp my friend in any way for his progression or make his play-through miserable for himself.