Nighmare Batman's role in GH is to help where is need and control points, so you need to be fast and be able to kill fast.
travel where you can't be seen and help allies that are 1 to 1 entering the combat stealthy and making 2 to 1.
Try not to fight one on one because NB is weak and he suvives because of the lifesteal.
So if the enemy somehow disable you and you can't attack you'll be dead.
Attack champions with low health, slowing them or blinking with you Ulti.
And more important in GH is to capture, so go fast to important points and defend your points.

Begin the match with some extra AD with Coda Blade (1),(2) and Lobo's Chain (1),(2) for some extra
health.
Save enough coins to buy Deathstroke's Claymore (1) and the Coda Blade (3).
Continue with the Soultaker Katana (1),(2),(3).
Complete the Deathstroke's Claymore (2) and the Lobo's Chain (3),(4) to slow enemies.
Begin the Velocity 9 Implants (1),(2) and the Atomic Axe (1), then Velocity 9 Implants (3) and then
Atomic Axe (2).
Finish the Items you have.
If enemies have lots of AD the you can buy Claw of Horus, and if they have PD buy Sword of Beowulf
If you think you don't need the extra life and want some fun with more lifesteal buy Cheetah's Claw.