SoulRider, not sure where you got that from, but there is no way that a R7 250 can play any of those games on medium/high, look here:
http://www.expertreviews.co.uk/graphics-cards/1305007/amd-radeon-r7-250
R7 250 playing Crysis 3 at medium settings gets an average of 17fps, which is nowhere near playable. This is a low end GPU, you're not going to be able to get smooth framerates on any of those games on medium or high settings, probably an average of about 20fps for Arkham city, and less for BF4, anything under 30fps is very unplayable. You might be able to run Arkham city on low and get 25-30fps, but thats a maybe, and same goes for Bf4 in certain areas of the map if you play a match with like 5 other players.
Point is, if you want to play any of those games, the 250 is NOT a good card. It would be fine for playing this like Minecraft and Counterstrike, and most older games, but you won't be able to play AAA games on a £60 card. You just won't.