The swamp isn't actually that hard, if you don't go after spawners early on and keep room to maneuver.

Bronze armor at level 3, a wood shield at level 3 and carrot soup, deer stew and minced meat sauce for food is plenty. Maybe carry a health potion with you for backup.

When you're fresh out of the Black Forest it is important to single out enemies and try to fight them 1 on 1. Keep running away if they gang up on you and use your bow to fire at enemies further away.

Wait for enemies to attack you and parry with with your shield. This will briefly stagger them and cause extra damage if you hit them. If you get overwhelmed block with your shield and try to get some distance.

A bronze sword at level 3 works very well, but for Bonemass you might want to use a bronze or iron mace early on. Using a sword against Bonemass will make the boss fight harder.

Once you got your first iron I'd craft a banded shield asap. Blocking and parrying makes the swamp a lot easier.

When you found turnip seeds, upgraded your cauldron with a spice rack and crafted some iron armor everything will go even smoother.

Lastly don't go into the swamp at night and make sure to always have your rested bonus. This is very important because otherwise you will be out of stamina constantly and it will take ages to recover, especially with the wet effect you will have in the swamp.