You just need to time it right and try to keep Nym-Foe from grabbing you as much as possible. Really hard, I know, but apparently not impossible.
If you haven't beaten her yet, I usually timed going through the pallets as Nym-Foe was moving onto the tile next to Jane. Better to trigger the pallet early and avoid getting caught than triggering it late though, so if you still get caught even with this, try moving through the pallets as she's moving onto a tile 2 spaces away.