I am also stuck here, even with the hint.
1. To clear the room I need to kill tar babies #2 and #3.
2. Tar baby #2 is trapped behind trapdoors and cannot be killed directly.
Therefore it must be killed by the mimic.
Hence, the mimic must reach the right side alive.
3. Tar baby #3 must be led out of its trapdoor area by Beethro (and killed).
Hence, Beethro must reach the right side alive.
4. To open the route to tar baby #2 for the mimic, one of the orbs in column 10 must activate and one of the orbs in column 24 must activate.
5. If one of the orbs is activated, its partner must be activated simultaneously or else tar baby #3 will be trapped.
6. If Beethro/Mimic activates an orb in column 10 with his pickaxe, then he will be stuck behind force arrows.
Therefore the orbs in column 10 must be set off with the powder kegs using the safety of the force arrows.
The only possible starting orientations for this to work are W, NW, N, NE, E.
This also means that the orbs in column 10 can only be activated once.
7. Each orb in column 24 can only be safely activated facing south:
This is obvious for striking the orb directly. It is also true for setting off a powder keg as the only safe standing position is on the force arrows, directly north of the powder keg.
The only possible starting orientation to activate both orbs simultaneously is S.
This is a contradiction!
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×Given that a starting orientation of E is valid, my logic in 7 is flawed, but I do not see how.