For Valus Ta'aurc...
[spoiler]come stocked with PLENTY of ammo resupplies, since you will have only limited chances to run out to refill ammo despite how much you'll be killing. 70% of the fight involves hiding in one spot.
There is a space underneath the far ramp opposite from where you enter the arena from, by where he first appears where you can get to that provides cover from Valus and his minions. there's a slot between the wall and ramp that you can just fit through. From here, you have three shooting positions; one over a window-sized opening in munitions crates that should protect you from Valus' minigun if you crouch. Another is a few feet away (remember to jump over the lip) that is a gap between two storage containers. Note: Valus CAN shoot you through this, but it's useful for pulling his fire away from the first firing position, as well as dragging away any crowding minions as well. The third is against the wall, and while it won't give you a line of fire on Valus' position, it will give you flanking shots into Phalanxes crowding your first spot, allowing you to clear out minions without Valus threatening you.
Using this spot, I was able to solo the Nightfall strike and the weekly strike after several tries. remember: Absolutely no rockets, and no grenades that can hurt you. (I.E., for warlocks, no Scatter Grenades and no Nova Bomb. I already embarrassed myself finding those out for you.)
When he moves away, you are free to jump out (Warlocks can make it by floating up the slot they jumped down). Phalanxes should stick by Valus, and any psions that spawn tend to hide on the far side, and should be a non-factor. Just play peek-a-boo with Valus around the corner, deal with any legionnaires advancing on you, and take time to gather ammo. Once Valus starts moving again (as cued by the music picking up) get back in your bunker and stay there for the rest of the fight. Pop ammo consumables if you get low (remember they all share a cooldown of 5 minutes), use your grenades like they're going out of style, and if you have a helmet that restores grenade energy on melee hit, smash Phalanxes in the shield! It counts! Though, this might only work with warlocks, no sure (their melee seems a bit further ranged than Hunters or Titans. Test at your own risk).
There are other methods, but I preferred this one for soloing Nightfall because of shielded psions and unflinching Phalanx Majors (thanks to Angry modifier). Valus is not the hardest part of that fight, actually.
That's pretty much it. With a little patience and perseverance, you can solo Valus on level 26 weekly and Nightfall (my current bests at level 27). Hope that helps for you folks who haven't done the weeklies yet and don't have a group of friends to do them. The REAL drag is trying to get through his lieutenants...[/spoiler]
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that spot is not really that good as people propose it. since there will spawn tons of phalanxes in front of you and you can't shoot the boss and i've seen Phalanxes glitch into the hide-hole and kill guardians. if you just stay on the right ramp and hide behind the three crates/covers you only ever have to deal with occasional Psions and Legionaries. both of them can easily be killed by throwing a grenade in front of their doors. The Phalanxes will stay on the bottom floor and NOT attack you. Sometimes Varuc comes up the stairs , stands there and shoots in your direction. but your are safe behind the crates. other than that you can easily peek out, take a couple of potshots and hide whenever he shoots back.