Martyr Logarius is one of the few bosses that I remember giving me serious grief the 3 or so times I played this game. At least he's skippable, not that anyone should. The other fight that gave me a lot of trouble was Rom the Vacuous Spider.
There were a couple more tough fights in the chalice dungeons which are completely optional and only worth doing if you really want to mine more fights out of the game. There was one giant flaming wolf boss in the chalice dungeons that gave me more trouble than ANY other fight in the base game or DLC, even Martyr and Ron.
As for the weapons, I never did a run using Kirkhammer or Whirligig. Whenever we get the inevitable PS5 version I'll try a Kirkhammer run. The first time I played this, I picked the axe since it hit the hardest. Everything was killing me due to being so slow. It was my first exposure to Soulsborne so I was trying to play it like a regular attack-spam type of game and it just wasn't working. I kept getting flanked and that would be it. So after a couple hours with no progress I gave up on the game and thought it was a POS. Turns out I was just approaching it completely wrong due to the lack of Souls knowledge.
In any case, I was going to sell it but ended up reading some info, like the cane being the best weapon for beginners due to the AoE crowd control mode. I started over with that, and actually made progress finally. Once I was able to get some survivability, I switched to the Saw Spear, then later the Tonitrus for the rest. I'd say Tonitrus is my second-favorite weapon, right behind the Blades of Mercy which I got in NG+ and used for all successive playthroughs (finally had the speed to spam attacks). Also used Ludwig sword quite a bit once the DLC was out.
That means there are a ton of weapons that I never got to check out. I can't wait to revisit this. I also didn't understand what Arcane or Bloodtinge did, and still don't. So there's still a lot to play around with. What a tremendous game. Best of the gen, IMO (but I haven't played DkS3 yet).