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At first I thought you were talking about the Independence Day flight-sim-type game, but that was 3D. More likely, you're remembering one of the "mission disks," which were very simple short games that came on floppy disks packaged with the toys. That sounds exactly like one of them, where you play as an alien bomber with the goal of destroying buildings while also fighting off human fighters.
There were quite a few of those "mission disks," I want to say somewhere around 18 of them. I have most if not all of them somewhere, so if you wanted further information I could possibly dig it up for you.

Some video games I played once or twice in the '90s.
1. Spaceship shooter thing with first-person (cockpit) view, on Windows 95. Included an allied ship you could shoot (prompting him/her/it to call you a traitor and return fire) and an early/intro cutscene involving what appeared to be anthropomorphic lions. (At least that's how another player characterised them.)
2. Spaceship shooter thing with third-person view on the Playstation 1 but was probably an arcade game originally (it had the "continue" feature that arcade games use to extract more quarters, though the number of continues allowed per game was capped in the Playstation copy). It had reasonably 3D-ish (maybe 2.5D) graphics, (admittedly of fairly low quality), the predominant flavour of alien spaceship was shaped kind of like an upside-down "U" and I think it may have come in a multi-pack with a vaguely similar game called "Jupiter Strike" but I'm not absolutely certain of that. Opening cutscene featured the "U" shaped ships destroying some spaceship or space station, and final game over prompted a cutscene of some alien figure laughing at you. This one is really driving me nuts because I found a picture I drew back then which featured one of the "U" ships.
3. Tie-in video game for the movie "Independence Day" in which you play as one of the movie's aliens trying to wreck a city. Success at this mission would result in promotion to custom-named ranks, one of which was "Talon Leader" or something like that. Required the player to switch between "bombing mode" to wreck the city and "shooting mode" to attack fighter jets trying to shoot you down. Required clicking to or bringing up a separate "map screen" thing to indicate which parts of a completely unchanging city background needed bombing. Purely 2D gameplay. Suffered from the Problem With Licensed Games with a vengeance.
4. Third person adventurey game for the Playstation 1 with what I believe was awkward PS 1 3D graphics. Offered a choice between 2 characters, one male and one female with no appreciable differences. Level exit point was a sort of crystal thing. The exit point for the first level would constantly change colour, and what colour it was when you entered it would indicate which level you'd be transported to next; the levels were grouped by theme, so entering it while it was, say, yellow would take you to "Desert World 1" and that would have an exclusively yellow exit crystal to take you to "Desert World 2" and so forth. The colour-changing exit crystal and the relationship between colour and destination world were explicitly described in the manual, along with the second-level exit crystal being static. Health/hitpoints were represented by four hearts at the top of the screen, with "half-heart" being the smallest increment of health/damage. There were "lives" on top of the health hearts and possibly "continues" but losing a life (or using a continue) would incur some penalty (having to restart the level, I think). Involved platforming, probably had had a fantasy story.
Edited by HangBrain