I'll point out that it was VADER in the TIE Advanced...who is easily equal to a squadron or two by himself.
Then there's the fact that every other pilot in that squadron was an elite veteran as well.
Nothing about the people flying the rebel fighters indicated they were extremely well trained or experienced.
If you include EU, yes. If taking the original movie as a standalone, no -- Vader just orders "get the crews to their fighters" with no specification that this is an elite unit, then tells two TIE Pilots to "come with me".
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Surface turbolasers shoot down one X-Wing, although the EU recontexualizes this was the turbolasers merely disoriented him and he crashed into the Death Star's surface. Turbolaser fire is both described and seen as generally ineffective against Rebel fighters, but does force them to maneuver evasively.
The six initial TIE fighters are seen to shoot down one X-Wing, and two TIE fighters are lost. This is not a favorable loss ratio,
but we also see that no X-Wing
ever outmaneuvers a TIE; both TIE kills came from a fellow X-Wing shooting a TIE off another X-Wing on a sloppy
ad hoc basis. We also see that an X-Wing's deflector shields can withstand only two-three hits from a TIE's rapid-fire guns, not the dozens of hits that the later video games allowed (while also taking away the rapid-fire guns). Vader kills three Y-Wings in the first trench run, two X-Wings in the second trench run, and one X-Wing in the third trench run, with his wingmen killing one X-Wing and damaging a second.
But we visibly see that only two X-Wings and one Y-Wing return home after the Death Star is destroyed, indicating that the four remaining TIE Fighters killed *every single other remaining Rebel fighter* while Lord Vader handled the trench runs. This is also consistent with the fact that the *only* X-Wings with TIE kills were the two best Rebel pilots, Luke and Wedge, and these were also the *only* Rebel pilots who appear to have any concept of teamwork (Luke was proactively covering Biggs and shot a TIE off him; Wedge shot a TIE off Luke when he was asking Biggs for help).
Thirty X-Wings and Y-Wings minus three survivors, three on-screen Y--Wing deaths and six on-screen X-Wing deaths equals eighteen offscreen Rebel deaths scored by just four remaining TIE Fighters.
We can break this down a little more by examining the Special Edition's expanded version of the panning shot of the Rebel fighters approaching the X-Wing: there are five X-Wings and four Y-Wings in front, fifteen more X-Wings and four more Y-Wings in back. That's twenty-eight Rebel snubs, with Red Squadron having eight X-Wings counting off prior to casualties and the other twelve presumably belonging to a second squadron. The Imperial count of thirty indicates two more Rebel fighters weren't visible in the shot, suggesting an understrength Red Squadron of eight, understrength Gold Squadron of ten, and a second X-Wing squadron of full twelve.
So four TIEs were fighting eighteen X-Wings and seven Y-Wings *still including ace Wedge and Force-sensitive Luke* after Gold Squadron peeled three off for the first trench run, and it's clearly implied that they killed at least five of the Y-Wings by the time the first run completed since Red Leader was ordered to make the second run and "keep half your group back for the next run", clearly showing that there were not enough Y-Wings left alive at that point to make a trench run.
In short:
Red Squadron had eight X-Wings, of which six were killed and two survived (Luke and Wedge).
Gold Squadron had at least eight Y-Wings, of which all but one were killed.
The second X-Wing squadron had at least twelve X-Wings, and was completely wiped out.
Two additional Rebel fighters, *most likely* Gold Squadron Y-Wings but possibly 'extra' unnamed squadron X-Wings, were also killed.
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That's "straight ANH". If you add EU/Legends material, then the extra Rebel fighters were definitely Gold Squadron Y-Wings since the EU established that Rebel fighter squadrons ran twelve-strength, and the completely annihilated X-Wing group was Green Squadron.
