Try this...

Have all of your toons stay in the Trophy Room (previous boss). With your main, start the event and go back to the Trophy Room. Wait 10 seconds and the boss will despawn. Run down to the end of the gauntlet, turn left into the room where all the mobs come from. Have one of your toons (not the tank) run back to start the event. When the event starts, tank everything in that room. Kill everything and loot the harpoons. When all mobs are dead, run out and use 3 of the launchers when you get the emote that says the drake is in range.

Be sure to pick up the boss right away and good luck!