The title of this article is conjectural as this subject has no known canonical name in the DCEU.
The Showdown in Smallville occurred mainly between Kal-El and, General Zod (very early in the confrontation), but later was mainly against Sword Commander Faora-Ul and Nam-Ek. The United States Air Force got involved to deal with the superpowered Kryptonian threats who laid waste to most of Smallville, Kansas. After many casualties, and much destruction to main street, the Kryptonians retreated and Kal-El and the air force emerged victorious. Colonel Hardy acknowledged Kal-El was not a threat, to which Kal-El thanked him, before departing. Thankful to have the alien for an ally, and in awe of the incredible power he displayed, the USAF give Kal-El the nickname "Superman".
Believing the Codex to be within the infant starship of Kal-El (which had originally brought him to Earth), General Zod, his Sub-Commander Faora, and Nam-Ek arrived at the Kent Farm to interrogate Martha Kent on the starship's location.
Upon finding the starship empty, General Zod angrily attempted to interrogate Martha further, but right at that moment, Kal-El himself arrived and violently tacked Zod away from his adopted mother. He proceeded to angrily beat Zod as he continued tacking him away at incredible speeds, until both of them smashed through a gas station, which lead to both of them getting momentarily incapacitated. As General Zod rose back to his feet, he noticed that his Kryptonian breather was broken, which lead to his extremely enhanced senses (now no longed filtered by the breather) overloading his brain, which, in turn, almost completely incapacitated Zod, while Kal-El gloated over him. General Zod was, however, saved by Tor-An, who momentarily knocked down Kal-El with a plasma beam from his Kryptonian Dropship, and carried his weakened leader over to the ship.
However, Kal-El's showdown was far from over, as both Faora and Nam-Ek had followed him and General Zod to Smallville, and now threateningly marched towards him with their fists clenched. Kal-El, however, despite knowing himself to be outmatched both in numbers and skill, refused to back down himself, and instead clenched his own fists and walked towards the duo, warning civilians to hide inside from the imminent danger.
Air Force Attack
However, right as the 3 mighty aliens were about to start their battle, Colonel Hardy and lead an attack against them with his USAF squadron, letting them know in advance that the usage of deadly force against the aliens was allowed.
However, the planes' high-caliber bullets, Maverick missiles, and anti-tank depleted uranium rounds only temporarily knocked down Faora and Nam-Ek (as Kal-El had flown out of the way), and enraged them, leading the superpowered evil duo to attack and slaughter the pilots. Just as Faora leaped to finish off another plane, however, Kal-El tackled her away, making them crash down in an IHOP store (where Pete Ross worked).
Superman's First Battle
However, Faora almost instantly rose to her feet and knocked Kal-El down with a mighty punch. He charged in to battle her, pummeling Faora with equally mighty blows, but her superior combat skill allowed her to dodge, counter and block every single one of them with ease, knocking the inexperienced Kal-El down again. Faora then proceeds to grasp him tight around the throat, and mock his lack of skill, claiming that her "evolutionary" advantage over the natural born Kryptonian Kal-El lies in her lacking a sense of morality. Faora then hurls her opponent all the way across Smallville into a bank vault, leaving Kal-El to pant in pain, and then telling him that history has proven that evolution always win.
However, despite being outmatched, Kal-El refuses to back down, and uses his main advantage, flight, to tackle Faora out into the street. Just as he is about to break through her Kryptonian breather with a mighty blow, however, Nam-Ek joined the fight, tackling Kal-El away from Faora, and pummeling him into submission, with Faora rising up and joining the beat down. Kal-El defiantly rises, grabs Faora and attempts to fly up again, but Nam-Ek leaps, grabs a hold of him, and forces Kal-El back down again. As Faora and Nam-Ek finally seem to have Kal-El pinned down and nearly defeated, he counters one of Nam-Ek's punches just in time, and violently attacks them with his heat vision, forcing Faora to loosen her hold on him.
With the US Air Force continuing to engage all three Kryptonians, the battle becomes chaotic. Nam-Ek engages the the USAF and promptly causes Colonel Hardy's helicopter to crash. As a member of the USAF falls to his death, Kal-El flies in to rescue him just in the nick of time, only to be brutally punched by Nam-Ek right afterwards.
Meanwhile, as Kal-El and Nam-Ek resume their battle, Faora watches Hardy's helicopter crash and then she proceeds to brutally engage and dispatch of the USAF members standing in her way with casual ease, utilizing her incredible strength and speed. As she approaches, a desperate Hardy unloads all remaining bullets in his gun on her, but in vain, as she invulnerable alien woman continues her approach. Refusing to go down easily, Hardy pulls out his combat knife. Amused as the human's defiance, Faora claims that "a good death is it's own reward", and draws a combat knife of her own before charging at Hardy.
Meanwhile Kal-El and Nam-Ek are trading blows of incredible might, while both are under fire from the surrounding US military forces. Kal-El promptly puts an end to the standoff by grabbing Nam-Ek, flying high into the air, and smashing his opponent with a tremendously mighty punch, which sends Nam-Ek flying several blocks away, causing a train to explode on impact, and temporarily knocking Nam-Ek unconscious.
Kal-El then intervenes just in time to save Colonel Hardy from Faora's blade, tackling her away from him with all of his might, smashing Faora into the road's pavement. This finally breaks through Faora's Kryptonian breather, which leads to her extremely enhanced senses (now no longed filtered by the breather) overloading her brain, which, in turn, almost completely incapacitated Faora, as it had earlier with General Zod. Despite her pain, a weakened Faora lets Kal-El know that he'll be unable to win, as vows that for every human he saves from them, she will so it it that a million more are killed.
At that moment, Nam-Ek recovers, and hurls a locomotive at Kal-El, sending him crashing into a building and momentarily knocking him unconscious. At that point, USAF planes fire a missile at Faora, and due to her overwhelming senses extremely weakening her, Faora is knocked unconscious by the explosive impact. Tor-An's Kryptonian Dropship then returns and shoots down the 2 USAF jets with plasma bolts. Nam-Ek then lifts Faora and boards the Dropship, which retreats back to the Black Zero.
Aftermath and "Superman"
The surviving USAF members surround Kal-El, who has regained consciousness. Grateful for Kal-El's help in battling the Kryptonian invaders and saving human lives (including his own), Colonel Hardy declares that Kal-El is not their enemy. The USAF members then lower their rifles, Kal-El thanks Hardy, and flies off.
In awe of the incredible power of their new ally, the US Armed Forces bestows Kal-El with the nickname "Superman".