Are you in a party? Did you remember to change the finish rule to anyone? Did you make sure to make the final finish attack after the stage ends (as Balor is disappearing)?
#[Exploit Weakness] Ultimate Strike
raw swift
fervent knot
So i just tried this myself, i soloed revived normal, got him down to around 5% then used way of the gun and got the checkmark 
how exactly are you doing the quest?
did way of the gun end at the last moment before you finished off balor?
lapis veldt
Are you in a party? Did you remember to change the finish rule to anyone? Did yo...
I was in a party with a guildie, and we did a normal everyday party. at like 5% I do the rest of the damage with WOG. does it need to be a "Anyone" party?
raw swift
One of the party settings is the "Finish Rule." The default setting is "Greatest Contributor" which means whoever the game thinks contributed the most (number of hits) gets the finish. If you set the finish rule to "Anyone in the Party" then any person can attack the enemy for finish credit when the enemy reaches 0 HP.
So you'll need to set the finish rule to "anyone" and then keep attacking until you get quest completion (one more hit after the boss reaches 0 HP)
lapis veldt
Aah dip, ill give it another go with that change to the party.