@.access:
Constraining all the Vinsmoke family by himself, easily blocking the offensive power of Bege's Big Father and constraining it despite how ridiculously big it is (3 or 4 times the size of the already gigantic Big Mom), taking Ichiji's attack head on and shaking it off with just a scratch on his cheek (unless you see the Vinsmoke kids as disappointingly weak as I do, in which case this is not worthy of mention), defeating Chopper and Brook at the same time with little to no effort and getting as close as possible to killing them if Pedro didn't act (well… killing Chopper, at least. I doubt Brook even breathes).
Don't forget him easily overpowering Pedro in combat right before Pedro set off the explosion
@Sereques:
What ticks me about the arc is the criminal underestimation of the SH crew. By logic, the SH rescue mission should be impossible if Yonkou live up to their hype. BM got attacked by the worst generations, Urouge defeated one of her commanders, news came through that Luffy invaded the island, a pirate that is considered the worst out of the worst generation, what did BM do? She sent Brulee (a fodder) to capture them and later thought oh yeah SH is the one that defeated Doffy, alright Cracker go and take care of him.
Then we have an assassination plan that assume a member of the SH crew in the NW is incapable of CoO and will surely be killed just because this guys are peanuts pirates? Can't they all take a moment and think why is our all powerful undefeated brother taking so long to kill this so called "child" pirate? Mont'dor with all that pen and writing stuff, I wonder what he's writing anyway.
Then we have Mr. I can see the future Katakuri who completely make mess of things. After he got wreaked by G4, then he was was like yeah I can see why my brother lost to you. I'm like seriously? Who cares how your brother was defeated? Point is the pirate in front of you beat your brother up, kill him.
Big Mom's actions when Luffy first came to the island were right on, not sure why you're complaining about that.
The Big Mom Pirates' plan to assassinate Sanji hinged on Pudding revealing her third eye and him being shocked by it. Shock = no CoO. And seems like they had at least two contingencies if it failed.
And now you're complaining about Katakuri? The fuck? The guy's only shown one total moment of weakness in the entire battle. And it's not like he would accept help from his crewmates, considering that he's stated time and time again that this is only between him and Luffy. That whole battle is the result of him not underestimating Luffy and knowing that failing to put him away would have consequences for them in the future.
Honestly, the fact that the Straw Hats have had to make SIX alliances with people associated with Big Mom (Pekoms, Pound, Sun Pirates, Firetank Pirates, Germa, and Pudding) to keep afloat in this mission, and despite all that Big Mom is on their ship, should be a testament to how hard it is to get around Big Mom, much less taking her crew on in direct combat. No Jinbe, and Luffy and Nami die in prison. No Bege, and no shot of rescuing Sanji's family. No Pudding, and no potential to satiate Big Mom. No Pound, and no way to get the cake out to Big Mom. It's easy to point and mock the BMP's failures, but the Straw Hats have had to give their whole effort and use their connections as best they can to stay afloat here.