How do I win the mock battle against the USS Republic?

I just started Star Trek: 25th Anniversary and apparently I'm so bad that I can't even win the mock battle against the USS Republic. After reading the manual closely, I figured out the controls and can last about 30 seconds in a battle with the Republic before being defeated. My methodology so far is:

1. Arm shields
2. Arm weapons
3. Turn on target analysis (can't figure out what this actually does)
4. Figure out where the ship is using the ship position monitor
5. Turn to face it (using the mouse)
6. Unload phasers at long range and photon torpedoes at short range
7. If I survive my first encounter and can't see the ship anymore, tell Scotty to repair the shields (if those are fixed, then stuff below it won't get damaged, right?)
8. Repeat steps 5-7

Invariably what happens is that I'm chasing the Republic, then it turns to face me and unloads its weapons. I continue to unload my weapons (like the "Fire Everything!" scene in Wrath of Khan), but it seems they always destroy the Enterprise (or at least, that's what the simulation says).

I figure that if I can't beat the USS Republic in a mock battle, there's no way that I can beat the real enemies in the game. How do I beat it? Or is this supposed to be a Kobayashi Maru no-win scenario?