Never read or watched Super Robot Wars (But I have seen some of the original Gundam series) but I'll give it a shot.
I'm copying and pasting what you wrote from the link:
“Sir, we are detecting unidentified Mobile Suits at 6 o’clock!” says an officer on the bridge of the battleship Ra Calium. (I would say give him a name. Even just like Officer Bob. Then elaborate on being on board the Ra Calium.)
“More?” responds Captain Bright Noa, commanding officer of the Londo Bell, “If these are Neo Zeon’s why were they not present when they were dropping Axis?”
The Ra Calium had not had much time to rest since that final battle between Londo Bell and the Second Neo Zeon. (I had to reread that for a second longer. It sounds at first as if Ra Calium fought against Londo Bell and the Second Neo Zeon. Maybe say something like "The Ra calium had not had much time to rest since aiding the Londol Bell against the Second Neo Zeon." Also, "rest" seems like too colloquial of a term here. Maybe say "recuperate". They had attempted to withdraw to Luna II due to being exhausted from their many losses during the conflict. These included Bright’s longtime comrade and friend Amuro Ray, (*gasp* AMUROOO!)who had gone MIA when he used his Newtype powers along with his unit’s psycoframe to prevent Axis from impacting Earth. However, on their way they had been redirected to intercept unknown forces that had mysteriously appeared. (I know this is fan fiction, but maybe describe in a quick sentence what Axis is exactly. Maybe?)
“Load the missile launchers for anti-mobile suit combat! Can we contact our units?”
“No sir, the interference from Minovsky particles is too thick for radio communication!”
“Damn, we’ll just have to hope they notice them in time! Fire the missiles to disrupt their formation when ready!”
The mobile suit, complement of the Ra Calium, and it’s ("its" not "it's") escorts were already in the midst of a pitched battle with other enemy mobile suits. These mobile suits, which unbeknownst to the members of Londo Bell were ZAFT GuAIZ R, resembled the Zeon Gelgoog to a degree, but had several different features and a grey coloration. Flashes of beam weaponry lit up the battlefield and beam sabers clashed with shields.
Then the new mobile suits got closer.
“It’s a Gundam!” said one of Londo Bell’s pilots as they saw the unit approaching.
“The enemy units are Gundams!? (Put the "?" before the "!")” asked Bright Noa when he saw the new units, “It is an Earth Federation unit?”
“There’s no IFF signal, we cannot confirm the unit's affiliation.”
“Then we have no choice but to presume it as hostile, continue the attack!”
The Gundams were actually the Destiny, the Legend and the Blast Impulse, piloted by Shinn Asuka, Rey Za Burrel and Lunamaria Hawke.
“The unknown warship is firing missiles, Shinn, Luna, evasive maneuvers!”
The three mobile suits broke off to avoid the attack. Luna fired her unit’s 20mm CIWS at the incoming missiles as the Destiny fires it’s ("its" not "it's")palm beam cannons as it’s (you mean "it")uses it’s ("ITS" not "IT'S")Wings of Light to deftly avoid the oncoming attack. The Legend launches it’s DRAGOON pods to intercept the enemy weapons, shooting several down, including those aimed at his allies. Finally Shinn blocks the last with the Destiny’s shield.
Watching this from the bridge of the Ra Calium, Bright Noa thinks back to those Gundam pilots he has fought alongside- Amuro, Kamille and Judau. Their movements- and the use of bit or funnel-like weaponry. Could the enemy pilots be Newtypes?
“Signal the Jegans to form up on the Ra Calium. We may need to withdraw in a hurry if these units prove to be too much.”
In the meantime the Destiny had intercepted one of the Jegans. Wielding his "Arondight" Beam Sword he cleaved through the mobile suit. As he speeded (sped - speeded is not a word) on past, the mech split in two as it’s (lmfao "its" not "it's")reactor exploded. Then the Legend’s DRAGOON pods propelled their way onto the battlefield and fired at several Jegan’s as well as the Ra Calium.
“Sir! There’s damage to the main battery and starboard mobile suit hanger!”
“Focus the defensive guns on those all-range weapons! Don’t let them sink us!”
“Sir, we’re receiving a signal! It’s the Nahel Argama! They want us to start falling back.”
The Nahel Argama was indeed approaching from the rear of the Ra Calium. It began firing it’s (you know what I'm going to say. . ) weapons at the enemy forces along with sending a laser signal to their allied battleship.
“Pass the signal to retreat on to our mobile suits and give them some covering fire. We are done here.”
The Destiny avoided a blast from the Nahel Argama as Shinn attempted to fire his beam cannon at the Ra Calium.
“Shinn, they are trying to withdraw! Let’s use this opportunity to let our forces retreat!” says Rey, whose Legend had just arrived behind the Destiny. At this point the Minerva was approaching from the direction they had come.
“But we can take them down!”
“Those are not our orders!”
“Damn it!” responds Shinn.
Both forces break off and retreat. The battered remnants of the Ra Calium’s mobile suit compliment land on the battleship. The ZAFT units land on the Minerva and the two groups start to move away from one another. After the Ra Calium and Nahel Argama get sufficiently away from the battlefield that the Minovsky particles no longer interfere with radio communication, the Ra Calium signals the Nahel Argama.
“This is Captain Bright Noa of the Ra Calium. We are grateful for your assistance, Nahel Argama. Do you have any orders from command?”
“This is Otto Mitas of the Nahel Argama. We were ordered to rendezvous with you and accompany you to Luna II. You will be leading a task force to engage a new threat that has emerged. Apparently an organization named CONSENT is engaging in a campaign to drive the Earth Federation out of the Sides. Apparently, they’ve even taken control of a few colonies already. We are going to try to avert a war, but if need be Londo Bell will begin combat operations against the enemy.”
“How can command expect us to fight in this state? We were already pretty beat up after the operation to stop Axis and this recent engagement has pretty much exhausted us completely.”
“You're going to be temporarily reassigned to the Nahel Argama. Also a couple of special units are apparently going to be assigned to your command.”
“Well, that’s something at least.”
The ships of Londo Bell continue on towards Luna II. On Earth another member of Londo Bell awakens...
Next time on Super Robot Wars Coreline: the White Unicorn and the Wild Bear of Russia!
So yeah - fan fiction. Like I said, I only somewhat watched the first Gundam series. Regardless, I treat any writing equally. I would say show us more the thoughts of Captain Bright Noa. Show us a slice of who he is by how he responds to what's going on around him, internally and externally. Right now the action is good - but I lost myself in all the references. Right now it's all "This guy said this and this happened. This guy now comes in saying this and this happened." Give us more of a scene by bringing us closer to the lives of the central characters.