I?m speaking from a Priest point of view, but these should apply to most classes.
1. Damage only one at a time.
If you?re extra careful the other two will never activate, meaning you?re only fighting one boss at a time. This is key if you?re a low damage or short range class. My usual sequence is Nut > Bes > Geb. DO NOT USE A CRYSTAL WAND YET, it?s far too easy to accidentally hit more than one.
2. Each boss has a sequence of progressively harder phases.
Nut: the key to identifying the phase immediately before the rush is the twin black arrows. The phase previous he only shoots one. I think this phase goes on for at least 10,000 hp, but don?t let the long stretch of time allow you to put your guard down. You can try using a Crystal Wand here since the artifacts spawned by Nut are essentially shields, but be careful not to hit the others.
Bes: artifacts (aka tacos or pyramids) are definitely going to get in the way here. Just steer clear of the orange boomerang shotgun (especially when it comes back!) and you should be ok.
Geb: the most annoying. The artifacts here do massive damage and like to get in your way. Plus the scarabs will paralyze you, setting up the shot for the artifacts. A Crystal Wand is definitely the best weapon for mowing down both scarabs and artifacts.
3. The final phase of each boss differs slightly.
Nut: STAY NEAR A DOORWAY. As soon as Nut rushes head for the door. He?ll chase you a bit, but the invisible leash to which all dungeon bosses are bound will pull him back. If you?re still using a Crystal Wand swap it out for a regular one. The extra range is really helpful finishing him off. Just jump forward, dodging slightly to the left or right to avoid the frontal attack, land a few punches, then retreat and repeat. He?ll do down fast.
Bes: he will charge if you get close enough, the back away. Strafing is the best technique i?ve found. Those boomerangs to the back are nasty, best be totally clear of that area as you retreat.
Geb: he?ll just back away the entire time while throwing artifacts and scarabs at you. If you get past Nut, Geb is much more annoying to finish off, imho. I like to approach him at a 45? path and perform a drive by shooting. He always takes the longest to bring down in my experience.