Tiger Road, port of the arcade game, but pretty different. 5 stages. Stage 4 has an alternate path and stage 5 has 2 alternate paths, and I think I take the fastest. Enemy spawns are mostly deterministic, they behave the same if you do the same thing, but a few things seem random. First boss is heavy RNG, in a savestate it seems like it can do any of the 3 moves based on how you move. I did happen to noticed I accidentally did some sort of crit on the first boss. There is some sort of frame if you hit them it does 6-8 damage and they fly back, but I couldn't find anything consistent with it.
I also do the monk mini games, if you do both you get double damage in the final stage. At least for RTA, it definitely seemed worth the time loss, the final boss is scary and slow without it. But it might be faster to fail the mini games for a TAS.
And I tried the PC Engine version and it's much harder, certain screens have a ton more enemies throughout, for example even just the 2nd screen of stage 1.
Stage 1 boss crit -
https://youtu.be/q1TuVhStads?si=vYPq6gInSq8V1e8H&t=442
RTA run -
https://www.youtube.com/watch?v=dBQpRbQP0Jo