As revealed through the story, Shez and Arval were essentially custom made for the sole purpose of fighting and killing Sothis, an outright god. They are both wholly incapable of dealing with Byleth initially, even without them having the Sword of the Creator.
Scarlet Blaze
In Chapter 3, Edelgard, using only Shez, some allied soldiers and much of the Black Eagle house (Hubert, Dorothea, Petra, and Monicanote Ferdinand, Linhardt, Bernadetta, and Caspar are all absent because the mission involves them potentially fighting their parents) mounts a successful sneak attack against Lord Arundel and Duke Aegir in a bid to reclaim the Imperial Palace from the influence of "those who slither in the dark". This works in large part because she ahead of time convinces Counts Hevring and Bergliez, who initially appear as enemies, to side with her and box Duke Aegir in to prevent him from escaping and to add their considerable power to the coup.
In that same battle, after the Count secures an escape route for his soldiers, he manages to go toe-to-toe with Byleth and hold them off long enough for you to actually cause damage to them (with the last two encounters against Byleth being a Hopeless Boss Fight and exceedingly difficult side mission, respectively).
In Chapter 8, if Count Rowe pulls a Face–Heel Turn and defects back to the Kingdom, Edelgard's response is very succinct.
"I see you've dug your grave. Now you can lie in it!"
While the final chapter of Edelgard's route in Fire Emblem: Three Houses only had her fighting Rhea and the remaining members of the Church of Seiros and Kingdom of Faerghus army who didn't die in the previous battle, with her promised campaign against "those who slither in the dark" left to be dealt with after the game's ending, the equivalent final chapter in Three Hopes has Edelgard taking on both the Church and "those who slither" at the same time, culminating in a combination of Sequential Boss and Dual Boss battle against both Thales and Rhea (who assumes both her Seiros and Immaculate One appearances during the fight).
It should be noted how badly Those Who Slither in the Dark are countered during Scarlet Blaze. Because Shez's abilities allows them to uncover secret agents, they are able to remove any possible threat swiftly. Not only that, but their attempts at distracting the main army fails: the worst they can do is stall for time, only for Edelgard to eliminate the last bit of corruption from them and then utterly dismantle them alongside the Central Church in the climax.
Chapter 14 of Scarlet Blaze is a battle between the forces of the Empire and Alliance vs the Church of Seiros and Kingdom. For those who greatly enjoy Claude and Edelgard as characters, it's awesome on it's own to see the two team up against Dimitri and the Church forces. Not only is the battle set to a great remix of Between Heaven and Earth, but takes place on Ailell, a great backdrop for a grand battle like this. Lastly the chapter begins with an awesome cinematic of the Empire, Alliance, Kingdom and Church forces getting ready to fight in a Mythology Gag to the three way battle in Houses - only this time, the 'War of the Eagle and Lion' is playable with the Eagles as the heroes.
It's even more awesome in the kill Byleth path, where Claude decides to betray Edelgard and the Empire with advice from Byleth, turning the entire thing into a three way battle. Unfortunately for him, Edelgard and Hubert actually catch wind of his plans, and proceed to plan around his betrayal, one strategy even involves using agents planted in the Alliance forces to cause more disarray, cementing Edelgard and Hubert are the real master tacticians in this route by outsmarting Claude. And once Claude is either defeated or killed, along with Dimitri retreating, Byleth shows up as the final challenge of the map. And victory over Byleth treats you to an awesome cutscene of Shez finally overcoming the Ashen Demon. Meaning it's entirely possible for Edelgard and the Black Eagles to fight Claude, Dimitri, Flayn, Seteth and Byleth along with their forces and come out the winner. The time has come to prove our supremacy indeed.
Azure Gleam
In this route's Endgame Chapter* It's 15 or 17, depending on if you recruited Byleth and got two extra chapters or not, you finally get the chance to kill Count Varley. After everything he put his daughter through, it is nothing short of cathartic to end the bastard’s life for good.
Even better, you can recruit Bernadetta before this mission, meaning that it's entirely possible to have Count Varley killed by his own daughter as payback for all the abuse he put her through.
You can also have Yuri carry out the deed himself as well, considering the fact that Varley had beaten him up years ago. And when Varley tries to bribe Yuri to spare his life, Yuri doesn’t take it, and carries on with his much-needed payback.
After the final battle, Thales, despite being beaten and on the brink of death, attempts one final attack on Dimitri: a massive barrage of dark magic. Dimitri, who by now is utterly done with Thales after everything he's done, both to himself and to Edelgard, simply walks through the attacks, even physically swatting one blast to the side, before running Thales through, finally bringing justice to the Tragedy of Duscur.
Thales: You cursed beasts will never defeat us!
Dimitri: You're wrong. This ends here!
Since Kronya also dies in the final battle, if you previously recruited Byleth and Jeralt (which results in Solon being killed by Epimenides), then this means that TWSITD's leadership has been completely dismantled, effectively ending their threat for now at least and avenging Nabatea.
Golden Wildfire
Claude and Count Gloucester's scheme to thwart the Empire's invasion of the Alliance. Count Gloucester defects to the Empire after the Alliance is unable to hold them off at the Great Bridge of Myrddin. Claude is forced to retreat to Derdriu, where the Alliance makes a last stand and manages to drive the Empire back thanks to Holst's timely arrival. After the Empire retreats and prepares to make another attempt to take Derdriu, Gloucester suddenly attacks them from Myrddin, trapping the Empire forces between Riegan and Gloucester and revealing his defection was all part of a scheme planned by him and Claude. The Empire forces only manage to escape thanks to Jeralt's mercenaries, and are forced to make a full retreat back to the Empire.
About halfway through Chapter 5's main story battle, the empire spawns in a slew of Wyvern Riders poised to charge after a mission-critical stronghold, with Claude expressing concern about the Alliance's ability to keep up. Enter Holst, spawning on top of said wyverns and revealing himself as a playable character. Not only does the man have an advantage against the axe-wielding wyverns, but his sword is a flyer-busting sword, so Holst absolutely gets to prove why he's considered one of the best, viaCurb-Stomp Battle.
In Claude and Lorenz's A support, after Lorenz says that the monarchy of the Leicester Federation does not need to be hereditary, Claude suggests that the next king should be chosen by the people of Leicester.
In one of the secret chapters in Golden Wildfire, Claude shows off his impressive archery skills, breaking up a fight between Edelgard and Dimitri by shooting an arrow between their faces when they are mere inches apart.
In Chapter 7, Claude's solution to dealing with Count Bergliez and the Ashen Demon is to lure them into the strongholds, lock them in, and rain down arrows on them. Even Byleth, who up until now has been completely unfazed by everything they've been up against, realizes they're in trouble and says they need to get out of there.
In the same chapter Holst and Count Bergliez face off in a duel in the midst of battle. Their fight is a cutscene and it does not disappoint.
In Chapter 10, Claude gets another opportunity to lure Byleth into a trap if you successfully complete the main missions. Since Byleth has been hired to assassinate him, he uses himself as bait to lure Byleth away from their client, Fleche, before dropping a boulder behind him to stop Byleth from reaching him. This gives the rest of the army time to defeat Fleche before Byleth can reach her.
In Chapter 10, Claude survives three people's attempts to kill him. Fleche hires Byleth to assassinate him. Claude baits Byleth into following him to draw them away from Fleche, and if the player is successful in protecting Claude, he escapes Byleth without having to fight them. Otherwise, Byleth is defeated and driven back by the Federation army. While Byleth is pursuing Claude, Myson appears from nowhere to try to kill him, but he is also defeated by the Federation. Finally, Fleche tries to kill him after Byleth fails, but she gets nowhere close before she is killed. In other words, Fleche, Byleth, and Myson all try to kill Claude in a single chapter, and all of them fail.
In Chapter 12, Hilda manages to rush in and block an attack from Dimitri meant for Claude, implying that Hilda has Super-Strength nearly on par with Dimitri's, since she blocks his attack with just her axe.
Paralogues
In Caspar and Linhardt's paralogue, "Like Cats and Dogs", they team up with their fathers to wipe out the remnants of Duke Aegir's rebel army, and then Count Bergliez suddenly decides to challenge them to a friendly "fathers vs. sons" contest of strength. Count Bergliez is said to be the strongest man in the Adrestian Empire, and Caspar, who once wondered if he'd ever be even half as strong, beats the two counts with Linhardt and Shez's help. If they complete the side mission where they capture more enemy strongholds, Leopold is so impressed and proud of Caspar for managing to surpass him that he passes on his sacred gauntlets to his son.
The Gatekeeper’s Paralogue reveals that Shez once got lost and ended up in the middle of the Battle of the Eagle and the Lion and ended up fighting all three houses... and won.
Arval's paralogue shows just how dangerous the Agarthans were during the war, and how close they came to winning. Your only playable character is Arval (in his past form as Epimenides) in a massive map—and you proceed to go One-Man Army on Seiros, Cethleann, and Cichol in their prime, along with hundreds of soldiers. Although it's only a vision of the past and you can't actually kill any of them, Epimenides is powerful enough to force three Children of the Goddess to retreat on his own.
