Ran it last night as an engineer, after much trial and error we found the most effective course was to choose your moment, slam buffs on, beeline it straight for the tornado dodging AOE and to try and get around behind and whale on it with high damage attacks from there. 

The tornado itself does no damage but it makes it tricky to see attacks coming your way. 
Don't bother with rez or repair - there's no point, if you get knocked down you're pretty much toast anyway. 

Still took a good while though! Best of luck people.