The Inquisitor was tough for me: I initially fought him and ignored the dragon, just chipping away at the Inquisitor. Many times he would "merge" with the dragon and his OP cataclysm spells would end it for me. I managed with enough wakestones but it took a while.
On subsequent trips through the BBI, I'd focus on the dragon and when it was dead (pretty easy, actually), go to work on the Inquisitor. This worked much better. With the dragon down, you can get a lot of hits in on the Inquisitor and it seems if you knock the dragon out twice (the Inquisitor eventually will resurrect him), the Inquisitor collapses allowing you a lot of time to do a lot of damage.
Additionally, blast arrows, strength buffs,and keeping your stamina full make the fight a lot shorter.
Tldr: go after the dragon whenever it's alive and take full advantage of the times the Inquisitor is down on the ground.