Upgrade a bronze pickaxe, weapon, and shield. Skip the rest and keep to wearing upgraded troll hide. Use your first trip into the swamp to figure out where to get some higher tier food ingredients and figure out how the fermenter can be useful to you. Once you have made some higher tier consumables you should be able to push through crypts with casual ease.

Once you have some iron use it to fill out your armour slots, before then working on another new weapon and shield for the next boss. It isn't until the next biome that it becomes essential to move onto iron tools like the pickaxe.