Axe is pretty good against the Elder for obvious reasons. It might take a bit longer to kill him in melee as opposed to using fire arrows from behind the pillars. The 2 handed Atgier special attack might also be good though I haven't tried that.

Perhaps if the vertical hit box isn't that high you could build platforms attached to the pillars and then melee him with the axe in relative safety as he stomps on the ground or summons his vines. This is how I deal with a certain large enemy from the Swamp biome. If he does continue to use his ranged attack this tactic wouldn't work.

Not only it is possible to kill it in melee.... that is actually the optimal way to do it.
Melee does far more dps than a bow and the melee stomp of the Elder is less dangerous than his ranged attack. You don't even need bronze armor, troll will do just fine.
Make sure to kill any roots that spawn near you but other than that just parry the stomp and hit the boss.

You need no bronze to kill the second boss... troll leather, flint arrows and fire arrows are well enough to beat the elder. You need some movement skills too.

Sorry missunderstood... If you're fast enough and you've got eaten well, it should be no problem in heavy armor.

Full upgraided tier weapon and armor is more than enough to kill that tier's boss. Bosses are huge, but their melee attacks are weaker than attacks of big mobs in same biome. They just have more HP and that's it.

Protip: Use the stone pillars of the summoning altar as cover instead of trees. Fallen logs can get in your way.

Watch out for the foot stomps if you melee only.