At legendary Tartarus can look almost invincible but I've beatten him, it's quite simple but a bit long when you know how.
I think the best weapons to fight Tartarus are the Convenant carabine/shotgun (some brutes carry)
There are only three valuable allies against Tartarus: a second player, Mr. Jonhson (the guy with the convenant sniper), and the elite with dual needlers
now to kill Tartarus...
-wait Mr Jonhson fire 3 sniper's shot in a row (while he does shoot a bit) 'cause it will remove about 90/100
of T's shield
-while he has no shield shoot him with a shotgun, a brute shot, or grenades (notice that his shield goes down for about 3,4 seconds)
-usualy after you damage T he stops and shout a warcry very loud (he's calling brutes), head for the top level of the platforms from here you are able to shoot the incoming brutes before they jump on the main platform
-repeat these steps until our friend T dies
One usefull ally was the elite with dual needlers, I'll tell you why if you are lucky this elite will shoot T, but there's a bug he doesn't need to reload (do you see it coming), so when he shoots enough spines there will be a little explosion wich will immobilize Tartarus when repeated many times, so if he could not move/attack he is a nice target incudong the needlers weaken his shield