I'm not arguing he's not competent. But the things they have him do and the villains they have him beat and with as few injuries as he sustains is just rediculous. Sure, every now and then he gets hurt significantly but it's nowhere near what it should be. It's not like he doesn't have access to powerful healing methods to fix it (which he would certainly use if the choice was keeping at his mission or being permenently incapacitated).
If Ivy ever gave it a serious effort she could kill him quite easily but they never go there because Batman HAS to win.