I have looked at the deal sites and to be honest I don't really see anything in your price range that would be capable of the Batman game on anything but low settings. As I stated above you really pay for a gaming laptop. It's not the time of the year for laptops to be on sale. Just like with anything electronic there are certain times of the year when the best deals are offered and right now does not seem to be that time for laptops.
I check these sites every day.
http
/www.logicbuy.com/
http
/slickdeals.net/
On Logic Buy you can use the tabs at the top to just search laptops.
Here is a graphics card hierarchy chart. Laptops are denoted by the Go ( mobile ) for Nvidia and Mobility or Integrated for AMD.
http/www.tomshardware.com/reviews/gaming-graphics-card-review,3107-7.html
Laptop makers put all kinds of features in the more expensive laptops but since gaming power uses batteries and creates heat generally only special gaming laptops even try to use powerful graphics chips. Battery power and heat are the enemies of laptops and dealing with those thing are why they get so expensive.
If you can look around for a week or two something may pop up. You can also try the Dell refurbished site. They have great deals sometimes and those units still have full factory warranties.
Sorry I could not be more help. Maybe someone will come along and have a great deal for you. These forums tend to be very helpful