I played this game on several Intel iMacs in MacOS 10.14 Mojave using the Mac App Store version. That is a 32-bit Mac application which will only work in MacOS 10.14 Mojave or earlier.
Batman: Arkham Asylum installs and runs on my M4 Pro Mac Mini, MacOS 15.1.1, Crossover 24.0.5 in a bottle which I prepared with "DirectX for Modern Games" before installing from downloaded GOG installation files. Unfortunately, while the game installs and runs, and the cutscenes play perfectly; there appears to be some audio processing issue which prevents the game video from running smoothly. The audio plays very slowly and sounds extremely "echo-y" and distorted, as if some sort of 3D effect or "spatial audio" effect is being processed but not working correctly. This appears to be the cause of the extremely poor performance of the video/graphics. This causes the game to play very slowly and with a lot of stuttering. It's unplayable like this.
I installed OpenAL into the bottle but that had no effect, positive or negative.
I also attempted to install and run B:AA using Porting Kit and the game installed fine from GOG installation files and the initial options panel comes up, but after clicking PLAY on the options panel the game fails to run and there are WINE errors behind the full screen game window.