There is a Change Battle Background event command. If you run that when entering the swamp area, and run it again when leaving the swamp area, you can have two different backgrounds depending on where you are on the map.
HOW you determine when the player enters/leaves the swamp area will depend on how large the entry area is - if only a few tiles, you could do it via events. But if it's wide open and would require many events, you'd probably be better off with a plugin that lets you associate common events with regions.