Are you sure it's really that condition? You must be really unlucky, because I think at those low stage at worst you will get is "your point will go down if the base is penetrated", not fail, but just lose points.
Anyway, that's basically a tower defense game, except that you're the only tower and the path is awfully short. A bunch of troop will appear in front of a blue base (which you spawn in from the start) and try to run into the base, and your job is kill them before they do so. These will repeat until you kill the required number of troop. If they successfully enter the base, they disappear and you lose points (or fail, if that was really the condition).
Pretty hard to do perfectly on most weapon really, since these troop won't wait for you and just run as fast as they can.
EDIT: and yeah, it doesn't have anything to do with base capture.