Batman Fight - A typical fighting platformer against Penguin and Catwoman
Let's talk about bugs
Batman Fight feels a little buggy. For example, 'instructions' button leads to level selection screen. Not to mention that the overall design can hardly be said to be polished. The Batman figure looks and moves exactly as in Batman Sin City and we've seen the same in many other batman games too. Sometimes it is not possible to collect batarang for no apparent reason. Lady with a whip can hit your through the walls which is not consistent with the behavior of other villains. The fact that you can simply avoid the fight and choose to jump over your enemy, or go different route and simply ignore enemies in dead ends, makes it all feel a bit unfinished and less challenging. Finally, I don't see the point of collecting starts. If it's about making more points I don't see the point of that as there's no store to buy upgrades or do anything with the money later on.
Lady with a whip
As we all know about Batman, there's only a human behind the black mask, so as being one he can easily fall into trap of charming and attractive maid with a whip. Don't let her good looks fool you. She'll whip your back and spend all your lives in a matter of seconds, so don't get too close unless you have spare batarang to throw right in her face.
Higher levels bring a lot of moving platforms, more complex maps and some new enemies. I am not sure about the guy with a helmet, so if you have a clue who he might be, let me know down in comments.