The swamp appears to have originally constituted an action puzzle for the player, which was later removed from the game. It appears that April had to jump from one tussock of semi-submerged grass to another, but some these mounds would appear and disappear at regular intervals. There were also a number of sharp-toothed water predators somehow providing obstacles along the path. It can only be assumed that it was impossible for April to die in this puzzle.
The only remaining reference to the puzzle is when, upon leaving the swamp, April says "There's an ordeal I'd prefer to not go through again" and "Did I drop something? It feels like I dropped something. Whatever it was, one of those... things... probably ate it." This lost item she refers to is her Delivery List.
It is possible to view part of the swamp puzzle by using the old .ini Hack. The area is not playable, and only part of the full image is visible. It is, however, animated and swamp noises are audible in the background. Interactive items have tooltips, and it appears each tussock was numbered. The highest visible number is 16.