Is it actually possible to beat those things, though?  I feel like I pumped tons of bullets into the giraffes, and while they changed color, I never managed to stop even one.

Huh, that's weird. You're supposed to shoot 70 bullets in order to kill the giraffes. The last color is the grey one, after that the giraffe makes a dead sound effects and it vanishes. The bullets move slow, so the best strategy is to get as close as possible (but not too close!), and just like in the original game, is better to stay behind the giraffe rather than front!