Ideas (I don't say that it's possible to implement any of them in the given time. It's just my intuitive ideas about this theme)
Immune system. Destroy the invader, do not destroy non-infected cells. In real life it's based on "antigenic markers", i.e. molecules that are not present on your non-infected cells. In game, it could be a 2D game with cell with small geometric forms and colors at their surface. The idea is : small and very similar. So the user would have a very short time to decide if the cell must die or not.
And you can widen the idea from this (for example instead of destroying the cell instantly you'll give the order "destroy" this, and immune cells will come to destroy it. So you have time to realize you made a mistake, but the order is still there. Then you have to select each immune cell and click "stop attacking !" to prevent the mistake to realize. But it take times).
Other idea. You have a bazooka and a slow-motion device (a slow time down device). So you can do rocket jump, but also destroy part of the environment to make obstacle on which you will jump or do rocket jump etc.
Think of super meat boy, but with a bazooka and destructible environment. The goal being to reach a certain point.
You can be imaginative on the theme, but I am not sure it will be accepted. For example you can make "destroy" and acronym.
D.elete E.rase S.uppress T.erminate R.avage O.bliterate and then Y.awn.
But I am not sure it would be accepted.
And in a more classic approach, I think you could do anything based on a wasteland/post-apo. Even better if the goal is to destroy the last remnants of the civilization for X or Y reasons.
I could just go on all the day long.
(I am not match to find stupid ideas :D)