If you just want to place swing components by pixel and don't want to worry about layouts, use:
Most people refer to this as null layout manager.
If you're going to do something like Soldat, first off you might want to check the projects on games.dev.java.net since I think there is already a Soldat clone underway. That aside, its a fairly fast action and effects packed game so raw Java2D is out. At the moment you'll find it difficult to get the performance you'll want from Java2D accelerated mode (due to some restrictions with alpha blending).
You might want to consider writing a sprite engine with either LWJGL or JOGL. There are a couple floating around but its not very difficult to do and there have been a few examples posted. Not to advertise too much you could always check out J2DA (in my signature) which is basically a 2D sprite engine over JOGL.
A map based on a pixel by pixel destruction!
The best editor I can think of would be Paint Shop Pro
Since you're doing pixel by pixel design, the easiest thing is just paint the level.