to swim across a lake or river.
across the lake or river is merely the goal.
Yes, you reach the other side, generally, unless otherwise specified.
Obviously,if you get a cramp and have to stop, you don't reach the other side.
On the other hand, you might just float there. Or stand up if it is not deep.
Presumably, you did not drown since you are telling us that you had to stop due to a cramp.
to [walk, swim, crawl, bike, hike, etc.] across body of water (swim) or land (the others), unless specified, means you reached the place.
Of course, you can also swim in a like or swim in the ocean or hike in the woods without involving any crossing to another place. You can also crawl across the floor (sprained ankle?) or crawl on the floor (not on the roof) or crawl in the garden as opposed to crawling in the road, but why would you do those last two?
You could be doing any of those and not make it to another place, other than to meet your Maker.