Episode 2 has Ledo and Chamber destroying the pirate ships and eliminating the pirates' asses from this universe. Literally.
In the third episode, he does it again without killing anybody. His dispatching of the pirate leader is noteworthy for consisting entirely of Chamber screaming at her to surrender while spinning her around, a funny contrast to the previous "vaporize everything" approach that shows that Ledo is willing to think outside of the box.
In the fifth episode, Ledo is sexually harassed and traumatized when venturing into the shady part of Gargantia for an errand. It's easy to imagine how frightening that must be to someone with no experience in earth life like Ledo, but he later braves them two more times in order to retrieve Pinion's mysterious box. By the end of it, his shirt is in tatters, and he's covered in lipstick, but he singlehandedly saved what might have been a very bland barbeque.
Episode 7 has a great one. Laser weapons are ineffective under water? Use your bare robot hands.
A minor but notable example: When Ledo gains strong evidence that Hideauze are capable of sentience and not necessarily monsters, he immediately refuses to continue destroying them as he'd previously spent his whole life doing. That's right. Ledo throws off a lifetime of brainwashing and grudges through basic moral integrity. Badass. A sign of his change is when he called them, the babies at least, "Whalesquid" not "Hideauze."
Most of episode 12, the glorious battle involving Ledo/Chamber, Pinion and Lukkage against Kugel/Striker and his cult.
Ledo defeats Striker by body-slamming her into a smokestack at full thrust!
Without Striker, the Cult is honestly curbstomped and reduced to wreckage in short order with zero losses on the allied side.
The ending of the second OVA. It might have been part of the beginning of Kugel's anti-Hideauze cult, but one can't deny how cathartic it was to have him to see through Aleria's false attempts to be the new high priestess and give the monster exactlywhat she deserved.