Gai using nunchaks may not be OOC but him continually bashing someone's skull using it sure is.
Gai never fought an opponent with regenerative capabilities before.
Tsunade survived Mabui's jutsu and is even shown no-selling Madara's Yasaka Magatama.
Mabui's jutsu only caused minor lacerations on her skin, while Madara's Yasaka Magatama were bite sized, only puncturing her in the gut. Nothing impressive, and nothing that would instantly kill her. Zabuza survived having dozens of swords in his gut, and he was able to run through an entire squad of soldiers with no arms and have final dialogue with Haku before dying.
No damage Tsunade has healed from has been shown to be instantly lethal. Yes,
eventually lethal if not healed, but nothing that would kill her before giving her a chance to regenerate.
Blunt force trauma wouldn't do much damage to her, the only things shown to have caused her damage where piercing attacks and so far Gai hasn't shown any moves like that.
Provide evidence that Tsunade's skull will not shatter when hit with Gai's boulder shattering nunchucks.
Katsuyu was shown tanking a full powered shinra tensei comparable to a nuke
She never took a focused Shinra Tensei head on. She took an AOE Shinra Tensei, which had the goal of hollowing out the village, not singling out a single opponent. Had she taken a direct one like the Gama trio, I'm sure she would have been severely damaged.
Regardless, Asa Kujaku generates flames. The fire will dehydrate the water on their skins via reverse osmosis, effectively killing her. And yes, it will dehydrate her given it managed to vaporize thousands of sharks as well as the tidal wave they were riding on.
While hirudora failed to kill a half-dead kisame.
Completely false statement, on so many levels.
1. Kisame was not half dead; he just finished sucking up Bijuu chakra from Bee, to the point Bee fell to his knees
2. Gai was not trying to kill Kisame; his intent was to capture
3. Hirudora occurred underwater, weakening it
4. Not only did it occur underwater, it had to travel through dozens of tons of condensed / compacted water in the form of a massive water shark, further weakening it
Hirudora did more to Madara's V3 Susano'o than the combined efforts of Tsunade, Raikage, and Onoki did to Madara's ribcage Susano'o.
In the off chance that it does kill the summoned Katsuyu, Tsunade can just call another one since the real Katsuyu cannot be killed directly.
Evidence that Tsunade can summon Katsuyu again? It's implied to be extremely chakra draining, given the combined efforts of her and Sakura only managed to bring forth 10% Katsuyu.
So yeah, Tsunade wastes the rest of her chakra summoning another Katsuyu, only for it to get fried by another Asa Kujaku.
Anyway all you have are assumptions while I'm basing mine on canon facts so unless you can actually provide a legitimate argument, I'm done here.
I've been providing a legitimate argument all along. You have been too neck deep in your forged fanfiction to notice.