In chapter 3, due to training under Luffy, Nami manages a rudimentary Soru against the Black Cat Pirates.
When Krieg threatens Nami, Luffy shatters his armor with a single casual punch.
Chapter 4: Nami defeats both Gin and Krieg on her own.
Chapter 5:
Luffy makes good on his promise to make Arlong eat his nose.
The Straw Hats demolish Nezumi's marine base, including Zoro utilizing Razor Wind to destroy ships from a distance.
In chapter 6, Luffy keeps up with Smoker even without using his Devil Fruit and obliterates him once he does.
Chapter 7:
Zoro, Nami, and Luffy get into a Body-Count Competition against Baroque works. While Luffy wins easily due to taking out all the mooks, Nami handily takes down Mr. 9 and Mr. 8.
When Robin playfully tries to take Luffy's hat, he appears right next to her with his hand on her head.
Chapter 8:
Vivi manages to dodge Usopp's shots, including the ones she can't see, hinting at possible latent talent of observation haki.
Robin gives Luffy a better fight than anyone else on the crew can, including Zoro.
Zoro shows hints of Armaments Haki in chapter 9 when he deflects an avalanche without touching it. Before that, Miss Goldenweek's Tranquil Green gives him insight to Observation Haki, allowing him to dodge Mr. 3's arrows before they even finish firing.
Nami beats both the herd of lapahns and Musshuru by herself.
Sanji manages to utilize Diable Jambe on Drum Island six arcs earlier than canon.
When facing the Baroque Works blockade, the Straw Hats utterly demolish each ship:
Robin uses her powers to break the bones of every crew member on one ship, then drops the anchor and spins the wheel while unhooking every heavy object, causing the entire ship violently clubhaul and sink.
Nami destroys a ship via Cyclone Tempo and Tornado Tempo to hurl their own cannonballs back at them.
Valerie simply crashes into a ship from on high at her maximum weight.
Finally, Luffy launches himself into one ship, functionally cuts it in half with his plasma, lifts up it's middle and upper decks, and then throws them so hard he impales a second ship with its masts. Then he blows up a third ship.
When Smoker attempts to arrest Luffy and Ace in Nanohana, both treat him as a mere annoyance at best.
In Chapter twelve, there are several:
Luffy, Robin, and Zoro manage to free themselves from Crocodile's drowning death trap. They do this via Robin getting all the civilians above in the Casino out of danger using her Hana Hana no Mi, and then Luffy kicks several-meters-thick ceiling through the top of the casino.
Robin, who never struggles in purely physical contests due to her rather unfair powers, has her usual tactic no-sold by Hina.
Nami and Vivi show absolutely spectacular teamwork against Sir Crocodile and actually manage to injure him to the point that he has a Villainous Breakdown out of sheer, practically incoherent rage. This cannot be understated. It was not Luffy. Not Zoro. Not even Robin or Sanji. It was Nami and Vivi, who gave the man an injury so bad that he states he's more furious at them than Whitebeard, and has him break out both Observation Haki and Armament Haki just out of sheer rage.
Zoro manages to once again tap into his Armament Haki, allowing him to defeat Smoker. For his part, Smoker invents a new technique on the fly after Zoro continuously overpowers his normal Devil Fruit techniques.
Chapter 13: Vivi awakens Conqueror's Haki, which she uses to stop both armies from fighting and forces them to listen to her. When Baroque Works agents try to incite the violence again by shooting, she immediately takes them out with some punishing strikes and exposes the entire Baroque Works conspiracy then and there by revealing the tattoos. The armies make quick work of taking out any and all plants in their ranks.
Chapter 14:
Nami defeats Mr. 2 despite being exhausted from her fight against Crocodile. This is after a hard fight where her opponent proves skilled enough to copy her Soru and tough enough to tank multiple hits.
Vivi successfully uses Ranyaku for the first time to destroy Crocodile's bomb, though not without sacrificing her leg. The next chapter reveals it to be a mess of shredded muscles and burst blood vessels. It takes even Chopper's medicine a good five days to get her back on her feet, which is an awesome moment for Chopper all on its own.
Luffy kills Crocodile. It's an even fight with both sides injuring the other. Luffy turns Crocodile's sand into glass and burns his real body. Crocodile uses his Haki to both dodge attacks and hit Luffy through his Logia defense. Crocodile even manages to hit Luffy with his poison hook, only for Luffy to reveal his devil fruit gives him immunity to such and keep on fighting with a hole in his gut. In the end, Luffy's final attack basically disintegrates Crocodile AND his final attack.
Crocodile death and Luffy's gigantic beam of plasma messes with Alabasta's weather so much that the entire country has heavy rain fall on it for days. By the time they make it back to the Going Merry, the nearly-dry tributary they left her in is basically full.
Chapter 15:
Robin finally gets to see Alabasta's poneglyph and learns that Pluton is in Wano. Luffy then drops a Badass Boast that they should never speak of it again even after they beat Kaido. He then does the impossible and prevents anyone from finding out the location of Pluton and defaces the Poneglyph, melting off Wano's name off of it in lieu of being unable to destroy it.
The Straw Hats fight and kill two Vice Admirals, though it takes everything they have to do so.
