Then you have Episode 6, where Gai takes down a mecha with nothing but some string and a Luger, and Shu combining two Voids to make some sort of gunblade powerful enough to completely destroy a falling Kill Sat. By the way, the design of a Luger pistol would be 131 years old at the time of the show's setting.
In that same episode, Inori suddenly busts out a pair of Glock 17s and guns down a squad of GHQ soldiers to cover Gai & Shu as they to stop the falling Leukocyte.
Dan punching Segai in the face even when covered in the cancerous crystals of the virus after Segai points a gun at Shu's mom. It's made all the more awesome by the fact that he managed to make his claims of disgust upon seeing Segai point a gun at a woman sound more badass than sexist.
Seeing Shu break through GHQ Antibodies' countless lines of defense with his friends' voids was pretty damn awesome. It starts as Inori sings the show's ending theme. Shu and friends are driving up to the barricade and Arisa's void deflects GHQ's outrageous machine gun fire; they follow up with Souta's void getting them through a wall, destroying the pursuing Endlaves in the process; Hare's void repairs an entire damn bridge while Kanon's void helps them find Inori; to top it all off, Yahiro's void let's Shu slice clean through Daryl's Endlave. It's all done with the spectacular animation and special effects this show is already famous for.
In Episode 13, when a group of disgruntled refugees attacks the school, Shu unlocks Ayase's void, which gives her cybernetic legs that grant super speed and agility. Working together, they both singlehandedly repel the attacking refugees and destroy the Endlave they brought with them, closing off with a Back-to-Back Badasses finishing pose. Even better, they do it in front of the whole school; the students' expressions are simply priceless - and probably somewhere along the same lines as the viewer's.
Episode 14 has Shu take a major level. He singlehandedly dismantles a student rebellion by, first, intimidating them away from Ayase and Tsugumi. Then, with Tsugumi's void (which allows the creation of remotely controlled clones of people), he proves to the entire student body that trusting the government will only get them killed. Finally, when the rebellion's leader pulls his gun on Shu, our boy (who was subtly backing close to another member of the rebellion) yanks out the poor shmuck's Void without knowing what it was without first making eye contact, throws it, disarms the rebellion's leader, and gives him the most intimidating stare we've seen all anime, with an appropriate non-fatal Bond One-Liner to boot! God damn, Shu.
In Episode 15, after Hare is killed, Shuu goes berserk Shinji-style and gains an upgrade for Inori's Void. Simply swinging it causes it to shoot crescent moon-shaped pulses of energy in whatever direction he was aiming. Even better, he manages to curbstomp Daryl, who's charging at him, while standing still and not even swinging the sword. He's just holding it horizontally, and Daryl's Endlave is cut in half, after which he shoots a sword beam at the two other Endlaves attacking them.
A villainous example: after presumed dead and left out of the loop for a majority of the story arc, Gai reaffirms his badassery through making an entrance on GHQ endlaves, then quickly incapacitating Inori before ripping Shu's entire right arm off, stealing his King's Power and rendering him weakened; he then uses his newly-gained power to create a missile from the voids of three students to destroy a UN aircraft sen to bomb the refugees, killing said students (two of whom, by the way, have been complete assholes up till now), and making it clear he is in charge; Overall, in a matter of seconds, Gai has reestablished his status as a leader in a matter of minutes.
Episode 19. To take a page from Segai's book: the Return of the King. Shu gains the third Void Genome, uses it to regenerate his arm, pull out Ayase's void, and and promptly uses it to wipe out an entire troupe of Endlaves. His flying around, dodging missiles and bullets is completed with a beautiful Animation Bump and a spectacular Curb-Stomp Battle. Shu has just taken the biggest level in badass ever.
Shu's line in the English dub right before he kills Segai is just the icing on the cake.
Segai: You're not a murderer. Admit it! Shu: You may be right. But I can learn.I'll bathe in blood if it keeps my friends alive.
Special mention goes to the unnamed UN Naval Fleet Captain in Episode 21, who shrugged off being infected by the virus in order to maintain command and a legitimate strategy against Gai's forces. This came just after Funeral Parlor Out-Gambitted the Ghost Troops.
This comes after Gai just managed to wipe out 87% of the UN fleet. There's just one problem for the GHQ: the remaining 13% of the UN forces keep fighting and provide vital support to Funeral Parlor as they are Storming the Castle. Had the UN soldiers not kept Arisa and her super-strong shield pinned down, things could have turned out differently for Funeral Parlor.
Shu's duel with Daath. Daath had about fifty mooks whose Voids he was drawing on, while Shu was using his own to call out his friends' Voids, but only one at a time. Combine with an Animation Bump to an already well animated episode, and you have the single best fight on the show. Shu wipes the floor with Daath. It was suitably awesome.
Shu: You don't know Inori's pain...None of you do...She fought her own ugliness inside herself, and suffered...And when I hurt from making the same mistakes, she supported me kindly. Only she stood by me, and believed in me...So this time, I'LL be by your side. This time, I won't let you go, INORI!!
Funeral Parlor's final battle with GHQ in Episode 22. When it looks like Gai and Mana are going to cause a global Lost Christmas and Gai is in the midst of giving Shu "The Reason You Suck" Speech, Haruka breaks through GHQ's defenses and corners Keido, her husband's murderer and the man that became an Omnicidal Maniac out of pure jealousy; Shibungi corners Kenji and gives Tsugumi the upper hand she needed to hack into GHQ's firewalls; and, lastly, Inori's song stops the global Lost Christmas and gives Shu the Void he needed to have a fighting chance against Gai. In the end, nearly every traitor and monster who worked for GHQ ends up dead. It it essentially one giant Kick the Son of a Bitch to GHQ. To top it all off, when it looks like Shu is going to sacrifice himself to save the world and erase the virus from existence, Inori also pulls one last Heroic Sacrifice to save Shu.