There’s so damn many, it practically has to be broken down by individual characters as well as by group. Both the battle at Chorh-Gom and the final conflict with Chao were rife with such moments for everyone involved. As for individually:
Tai Lung: Rejecting Chao in his cell. Taking Po by surprise and technically defeating him (with the nerve strike no less!). His utter smackdown of Xiu in the final battle. His Rousing Speech. Forgiving Vachir. Making up his own new style of battle by mixing up all the other styles. His use of fire chi, of course. And killing Chao.
Po: Cleansing the Sacred Pool. Defeating Xiu at Wu Dan. Realizing he still has much to learn and becoming a true Dragon Warrior. When he knocked sense into Tigress after the birch forest. Working as a perfect teamwith Tai Lung in the final battle. And right at the very start of the story, actually intimidating Tai Lung and making him flinch after the snow leopard insulted Ping's soup, and only by using words and a firmer tone of voice.
Tigress: Her entire performance in the final battle, particularly her usage of the Ninja Weapons, her defeat of Chun, and truly releasing her full strength and anger—which got to the point of actually scaring Tai Lung into never making her angry. Killing Vachir as well as owning Xiu at Wu Dan. Her verbal smack down of Shifu and his parenting skills, or lack thereof.
Viper: Getting Po out of his emo state of mind in the final battle. Her performance in the battle against the Wu Sisters. And her entire plan to get Tigress and Tai Lung together, since in the end it does work—it’s entirely possible they might not have ever gotten together without her (and Mei Ling's) help.
Monkey: Not only does he resist Chao’s More Than Mind Control when he attempts to reinstate it, but he later fights off hundreds of demons with the Iron Fist and a pair of nunchaku, which at one point he wields with his tail. Sealing the gate to the yaoguai's realm was also quite stunning.
Crane: How he finds evidence to prove Tai Lung’s innocence, then arrives Just in Time to save him from being hanged and reveal the truth. His fight with Chao also counts, particularly his use of the Wronski Feint and concealing one of the Ring Blades beneath his tossed hat.
Mei Ling: Her You Shall Not Pass moment on the steps of the Jade Palace, where she defeats both Chun and Xiu. Her exoneration of Tai Lung at Yunxian. Her defense of him at the trial, complete with staff play. And in a cross with Crowning Moment of Heartwarming, when she succeeds in convincing Jia, after learning she didn’t kill their father, to do a Heel–Face Turn and fatally betray Xiu.
Shifu: Threatening the possessed Fu Xiao with a chi-raised boulder at the trial, and his subsequent exorcism of the Valley’s citizens with Oogway’s staff. The entirety of his battle with Chao. Getting Wei Chang to incriminate himself. And you could say the entirety of his clever program to teach, and redeem, Tai Lung.
Oogway: In flashback, his fight with, as well as defeat and imprisonment of, Heian Chao.