(As time goes on I'll add pictures and stuff to make it look fancier, so long as people think positively of this guide.)

Gotham still needs The Batman.

My Batman style is pretty simple. Burst assassin with amazing cape flinging skills.

Most people tend to max Batman's Q before his W, where as that's fine for Divided when top laning since you may want a large poke, it won't do you too well for Gotham Heights. Your W's dash, low cd, on hit effects, and the base damage just makes it the best skill ever.

The Optional Item list I used as a seperate build, it's better if you want a bruiser batman as opposed to an assassin. You can mix and match as you see fit to better help your own style.



 Build Order
The order is a bit situational. If they're building up tons of armor, then finish Atomic Axe as soon as possible. I tend to finish my items in the same order, with a few exceptions.

[[Deathstroke's Claymore (1)]] and  [[Rip Hunter's Time Pack (1)]] as my starter items. Build up your Time Pack to level 3 asap, then finish off the Claymore, picking up Soultaker Katana (3) somewhere between Claymore(2) and (3). You'll want to get the Katana pretty early on so you're getting the endgame benefits as early as possible. Coda Blade and Atomic Axe should be the last items you pick up, as they're more late game items. If you really need the armor pen though, Atomic Axe should come first. Coda Blade (4) is kind of situational. If you're enemy team has a lot of Healing, and a lot of armor..Coda Blade is utterly perfect. If they don't have a lot of healing and armor, go ahead and pick up [[Joe Chill's Revolver (3)]] instead, since a good crit on your W can be the perfect initiator in a team fight.


Stolen Power

[[Supergirl's Invulnerability]] Is a great choice for Batman, as you can use it right as you dash into a fight with your W, and then you get a nice power boost for your E and maybe a basic attack or two if your shield lasts.

[[Atomic Wonder Woman's Super Speed]] is another great choice, as it makes you run faster while wandering or even chasing down those squishy targets. It also gives a nice damage boost when used right.

[[Poison Ivy's Healing Wave]] This is a fantastic choice as it has a slightly lower cooldown than Invulerability and gives you the same attack boost as the shield, in some instances this is the better choice, as you can heal allies and you keep the power boost for a fixed 5s and isn't reliant on your shield remaining in tact. Personal preference I suppose, since the healing wave heals less than the shield absorbs. 


Team Fights

When you're in a team fight throw a few batarangs until someone on either team initiates a full fight. Always jump in with your W to begin the fight, you'll want to hope you get a nice crit and maybe heal up some poke damage from the initial strike. Try to jump to any squishy targets and burst them down for your team to pick up the kill, or try to take it with a quick Q as they try to run away. Since I tend to keep my Q at level 1 for a while, I don't ever expect it to pick up a kill and I tend to have to chase down with W after a new charge comes up if I used them all.

Chaining your skills together properly to get as much damage as quick as possible is what you need. I wouldn't worry about your Q in your skill chaining unless they're too far for a basic attack or your W doesn't have any charges left. W->Basic Attack->E->W->Basic->Q tends to kill most squishy targets when you've got yourself built up. If you can get away with it you can use your W to dash between targets and deal a nice chunk of damage to everyone for your team to pick them off.

(Swearing warning)
I will not be able to say this enough; There are only a few reasons as to WHY you'll be attacking a tank.
1. If they're the only one left.
2. If you're using a W on them to use a second W to jump to a squishy target.
3. To bitch slap Superman and let him know how much of a little pansy he is, YOU'RE BATMAN MOTHER FUCKER.


Amplifiers

Mods:
-Enhanced Attack Damage Atomic Axe: +10 Attack Damage (Tier 1)
-Enhanced Cooldown Reduction Deathstroke's Claymore: +5% Cooldown Reduction (Tier 2)
-Capacity Soultaker Katana: Increased maximum Attack Damage Collector (Tier 3)

Augments: 
-Kord Industries LASER +3.02 Movement Speed and +2.01 Attack Damage
-Queen Industries COLUMBUS +0.3 Attack Damage/lv (Max 5.7) and +1.5 Attack Penetration
-Queen Industries KAI +2.41 Attack Damage and +1.5 Attack Penetration
-Kord Industries HORSEPOWER +1.8 Attack Penetration and +3.02 Movement Speed

I find the +6.03 movement speed to be just enough to make you a little faster than most squishies, which gets you in range for a W and then the rest of your burst. The rest is self explainitory I hope.

The End~
I will update later on about matchups after I do a bit more 1 on 1 research with various champions. I hope you all enjoy this guide and I really hope it helps. A lot of this can easily transition to Divided laning, but if you all like it I will post a laning portion, and possibly a jungle portion. Thanks for reading.