Nightmare Batman was hit with a pretty heavy nerf, and because of which, his build has changed dramatically. He is no longer the squishy destroying, 100-0 monster he was in the past, nor is he the super potent duelist he once was. In fact, Nightmare Batman's primary focus now is almost a 'supportive' role, in that he does moderate sustained damage, and has a long range, long duration hard CC that will allow his team to follow up, or allow him to pin down an enemy diver.
Amps: Bruiser: Jungle Sustain. You can also try Assassin: Early Terror if you want to rush a Coda Blade, but it's not as effective as it once was.
Skill Order: Start with Q, max W. Q is better for the potential level 1 fights, lets you check bushes from a distance, is all around a better utility spell. W, however, has a dramatically increased jungle clear rate, and as strange as this seems, is better now for ganking than Q is. W does enough damage that, with proper placement in a lane gank, can either force an enemy to walk around, or deal significant damage as they pass through. You don't so much want to drop it ON them early game, as much as you want to drop it behind them and force them through it, or use it to wipe out the creep wave so you aren't taking that damage. Reasoning behind this major change is the lack of energy restoration on Q hits, and lack of flat armor pen to buff Q and auto damage. All this said, you are better serving your team by staying in the jungle and power clearing/counter jungling with cloud until you hit 6. At 6, you want to get into lane ganks in a way that you can bite someone in your rank 3 bat swarm (which, when you are forced to take the full duration, is very considerable damage), and don't forget to drop your meteor under them beforehand. Meteor + R + W should be more than enough to finish off a wounded enemy, or do enough and hold them still long enough that nearly any ally will be able to finish the job on a full health enemy.
Q after W, energy cost reduction. Passive next, but only because your E is pretty weak now. It used to give AD, Armor Pen, and Move Speed. He already has high base movespeed and has little trouble sticking to targets, so it's essentially a high cost steroid, on a character that already has energy issues. Better off playing more as a stealthed initiator, and using E to finish people off, or run away. It's also worth noting that in the October update, all attack speeds were lowered and attack speed per level was increased, so Nightmare Batman's E is actually harder to keep up at early levels, and is actually near impossible to get the full duration out of at early levels, even on stationary jungle creeps. Further reasons behind the W max.
Items: Another area where Nightmare Batman has gotten heavy changes. Marauder's Knife, Marauder's Shield, 5 pots. You can also go Hawkman's 1 and 2 pots, since you have the Marauder's Knife cost reduction mod. Rush your way to a Fragment of Mogo level 3. You can use this item in conjunction with your normal Meteor Bite combo, and the stats on it give you the strength to tower dive early gave. Immediately after Mogo, Spear of Destiny. This build is, essentially, a combo and bounce style build. Raw AD from spear, power armor. Your ultimate is 1.0 AD per second for 2 seconds, raw AD is king. For this reason, next item is Atomic Axe. From here, you have options. The fact that you already have Spear of Destiny means that you can build more tank items, without falling overly behind in damage. That said, late game, you won't 100-0 on your own anymore, you ARE, however, a stealthed initiator that can facilitate a pick on an overextended enemy with ease, leading to a wash over 5v4 in your favor. Build whatever you think you need from the optional items section based on per game needs. That Fatality's is not an accident. It amplifies ALL damage you deal to that target by 10%, after dealing 15% of their current HP. This item (and Mogo) can be used WHILE channeling your ultimate, and since your damage isn't all frontloaded, it's totally acceptable to Meteor, Bite in swarm (note: late game, swarm damage isn't worth sacrificing a good bite for), Lance, Mogo. This will amplify your mogo and meteor damage, and more than half of your ultimate damage assuming you are fast enough. It is a great deal of buttons to hit, with a heavy reliance on positioning. It's a bit of a mechanical challenge, and takes some practice.