As the title says, I finished the game in a no-bow run, all of it after the boss buff patch.
Eikthyr: 20 minutes in, I made a flint axe. Happened to get 2 deer trophies and just did him still in my basic rags, with tail+meat+shroom for food.
Elder: Some basic, mostly unupgraded troll armour, a bronze axe tier 2 and a bronze buckler. Parry the stomp and whack away until another stomp, rinse and repeat.
Bonemass: Still in troll armour, but with iron helmet. Iron mace and shield t2, some face-tanking and some kiting to regen health. Because of the constant rain even honey+rested can keep your health down if you don't dodge most of poison puke, who knew. Hovered at low HP a lot, but playing smart let me wait for mead cd and still deal some damage. Did flatten a large area for the fight to avoid deep puddles screwing me over.
Moder: Got maxed silver armour, fang spear and iron atgeir for this one. Lots of enemy spawns near the summoning platform, so golems, wolves and drakes would help her out. Took a solid ~30 minutes to win. Ran out of mead and was extremely close to dying before managing to take her down. Sometime during the fight I missed a spear toss so I only had the atgeir to damage her when she was on the ground. Had flint spear backup, but only used it to deal with drakes.
Yagluth: Just over 4 hour grind to get all the totems, blackmetal and flax for maxed endgame gear, along with food. A full 4 minute fight of whacking him with a blackmetal axe and face-tanking all the damage. I out-regenned all of it, and even used tasty mead (so I had less regen).
On a difficulty scale, Yagluth might be the easiest all things considered, because at least Eikthyr *could* kill me, though if I'd made any armour at all then Eikthyr is worse just because it is even quicker to take down. Elder is also down there on Easy AF, but a bit more difficult as you do actually have to block, and the roots can spawn in ways that you either move or get slammed (and quite possibly die). Bonemass was of mediocre difficulty, felt like a boss fight (deal with adds, then boss, dodge, manage pots(mead), kite etc.). Moder was a challenge. Her health was high, and her attacks hurt. Luckily you can easily dodge and parry her melee attacks, but then you might lack stamina to hurt her, so you need to keep on your toes. For me the adds of the area did not help, and made it much harder. Without adds she is a little stronger than bonemass, but at around the same tier.
Note: THE hardest part of the whole playthrough was getting blackmetal and fulin totems. If you take it slow (kill roaming fulins only) it is easier, but I wanted to see "how bad is it to take on a camp?". Hard.
Death toll of the run:
Meadow – Day 1, tree. It went bruce-lee on my ass.
Black forest – The first and last thrown troll rock to have hit me. Was a 1-star troll, and that rock hit me square on the face.
Swamp – Poison resist ran out, blob on crypt ceiling went "hi" immediately after.
Mountain – Was mining a golem, he pushed me off in an attack that also broke a big piece of a rock we were on. Fall damage got me.
Plains – Double fulin fun, once burning to death after 1-star torch-guy smacked me, and a second death from a sniper (spear) as I was trying to handle his friend's attack on my farm.
TLDR: The game is fully doable without bows, but especially Moder is noticably more difficult. Cannot exploit her getting stuck, as you need to go up to her to deal solid damage. Eikthyr, the Elder and Yagluth are still pushovers.