Don't bring tanks to Nyzul.
Nyzul is pretty easy, especially if you have APRadar.
Your PT format should be 4 DD (1 of them being a versatil DD like BLU helps) and 2 healers (mix up healers, 1 RDM and 1 SCH, or 1 WHM and 1 RDM).
The only difficult aspect to get at first is lamps. Lamps require someone leading the run to make sure it's not disorganized. There's 3 concepts to lamps, click 1, click all, or click order. When you enter the floor it will just say lamps. Tell everyone in the PT to go find a lamp (sneak and invis up, avoid aggro), first person that finds a lamp clicks it, it will say whether all need to be clicked, a specific order or just the 1. If it's the 1, everyone has to click it. If it's all, then you need everyone to go find their own lamp, stand by it, once everyone is at a lamp, call a time and everyone clicks it at that time. If it's order, you do the same thing as all except before calling a time, you announce an order first (say there's 4 lamps, announce a random order with the people's names (Mike, Tom, Joe, John)). You tell people to / when they've clicked it, so they all / in order. Then you tell them when it turns off. Joe and John say off. So what you would then do is call the order Mike, Tom, John, Joe. That will work. It's the lamps that go off that were activated in the wrong order. So if Tom, Joe and John say off, it will either be Mike, John, Tom, Joe or Mike, Joe, John and Tom.
Does that make sense? Once you get the above Nyzul is easy as all other floor types are either kill everything (why 4 DD 2 healer system is best) or kill the non-NM IT mobs (a family (i.e. all imps will check IT or all cockatrices will check IT), a single mob (a random normal mob will check IT) or a leader (a NM that isn't a NM outside Nyzul).
Edit - Oh yeah and exit after clearing every 5th floor. I've had it twice where someone selected to go up instead of exiting and we lost.