Just like the Grey Dwarves and Greylings, the Elder (their king i guess??) is made of wood and therefore burns quite well if you use fire arrows against him. The pillars around the summoning area are great for avoiding his "ranged" attacks, and when he summons the roots, simply run to a different pillar, duck behind and shoot him with fire arrows before he shoots the vines at you again.... repeat... Pretty easy boss.

Just for general information... I am not telling anyone how to play, but Bronze armor is somewhat a waste of time and materials (at least right now), as you can survive just as well (or better) using upgraded troll armor, which has no movement penalty and therefore doesn't drain stamina nearly as fast as bronze armor does.
I often use Troll armor throughout the game until after completing the swamp biome, and have no problems running across the Plains biome wearing troll armor, if I'm just passing through... It's pretty good armor overall.

The Bronze ingots are better spent on bronze tools and weapons, and I DO understand the tendency for people to craft all the bronze armor, as it actually LOOKS like your first "real" armor, but just pointing out that it's very possible to survive just fine with upgraded troll, especially since you can move / run / evade mobs much easier without losing as much stamina. MANY people skip the whole Bronze armor thing as it really isn't worth the time or effort.

Poison resist potions are the single most important thing for the swamp. They have to be taken BEFORE you get poisoned so you want to bring a stack and always have them going as a single dose of poison from swamp level critters can do 70 damage from no star stuff without poison resist. Which means sitting by helplessly as you die if you don't have poison resist going. With poison resist it's knocked down to less than 20 damage.
Aside from that park your boat safety and bring portal supplies. When you need to unload/resupply/repair (non-ore stuff) pop home via portal. All your scrap iron should go into your boat untill you have a ton/cleared the area then you can sail it home. The safest spot for portals is going to be on top of the swamp crypts.

Look for abandoned houses, beehives are in there. The honey is useful for potions and also serpent stew if you bag a sea serpent.

Get a lot of flint arrows. You can then stand on the other side of a column when he uses his ranged attack to block most of the projectiles. When he summons vines from the ground, sprint behind the next column and repeat. Its probably a good idea to put down a portal nearby as well.

I'd say to try to find villages on other islands meadows then (to search for beehives), because honey is used for all meads + recovers health faster then other food.

Other than making some potions for healing and stamina (and poison resistance for the swamp later), you are ready.
Btw you can kill him much faster in melee than ranged, just block his stomp, move away from or kill the roots he occasionally summons and that's it. Only bother hiding behind a pillar if you get low on health and your healing potion is on cooldown.
Other than that, just get rested, clear the area from any enemies before summoning him and start the fight during morning.