Hitting the helpful owl

Game, tall pedestal islands. Main character is a woman, aided (though arguably unnecessarily) by a fellow high-ranking male crew member from whencever they came. Hit the helpful owl off before moving to the next island, and that island's owl will leave to help him so you can get a bonus apple. Main challenger takes us to his ship (Firefly theme). They are watching Star Trek TNG and we see the saucer section get blown up by something. Then it switches to TOS, we get a shot of the ship, then a shot of the bridge. Then the bridge crew comes out of the screen.