Take an anti-poison potion right before landing there. Main poison enemies – green jumping jelly things and leeches in the water. Use your bow against both. Also, you can raise flooded ground with your hoe and avoid sudden leech death syndrome.
Search for crypts located on the swamp shores (stone structures with green fires) collect iron, and 10 withered bones to summon the boss. Don’t ignore green growths from the trees: build a ladder and chop them with your ax. Three trees should give you enough guck, an additional component to make and upgrade late-game bow later, after mining some silver in the snow biome.