To enter the room, you'll need to back into the room on the bottom space. Then you can use the splitter to move up one space while still facing away from the first medusa. Normally you can't step backwards - but the room transition allows it.
Beating the level takes advantage of three game mechanics:
- Action order in a turn seems to be: Move -> Reduce move counter (and kill cats if out of moves) -> trigger conveyors -> trigger splitters -> trigger medusas, with any cat on a flag after any action triggering the flag.
- Splitting doesn't change direction
- Dead cats don't get stoned
More specifically, you'll need to move the flag into a position where you can get one dead and one live cat, then revive and sacrifice the dead cat to revive the final cat.