I'm sure there are alot of Batman Guides so i'll keep this short and simple.

The Key is the stolen powers as they'll help you take out the speed and health camp early. 

I usually save the stolen powers when clearing enemy camps, after clearing my own.  I'll look around and if they haven't cleared the large camp yet i'll wait for them in stealth and nail them.

Get an early "E" skill and make sure you up your "Q" batarangs as fast as you can.  

Key items to start are the Maurader Shield and Knife.  Which should be replaced for Lobo's and Coda Blade for your ganks (start asap, the more psycological fear you put in them, you win).  

Batman thrives in this role cause his passive also gives him the advantage of hiding in stealth and hitting at the right time. 

my combo is "W" -> autoattack (until they run, or x2-3 times) -> "Q" (sooner if they run) -> "W" again when available -> auto attack

Save your teammates with a well placed "R" , or if you have lobos, using batarang "Q" and hitting them will slow them greatly. 

The chase works on the same principles, his "W"'s reach is quite large once targetted, so start with "W" and use "Q" to further slow them down (after second hit).  

That's it, otherwise depending on your team, go for ADC items (Joe Chills, Velocity 9's, etc) or tank items depending what your team needs.

Good Luck!