It depends on if you just want to consistently beat it, or consistently beat it fast. The TIEs come in waves that use two types of flight pattern. When each wave starts, just hold up and right and fire away. The TIEs that come in from the bottom right will fly right into your fire power, while the TIEs that come in from the bottom left will go to the top and eventually move to the right where the other TIEs are/were. That's about 15-20 basically free kills. After these guys are toast, the TIEs will come in groups of three and try to fly in front of you while shooting torpedoes like crazy. You don't HAVE to kill these guys if you don't want to (although you need to kill a certain amount of overall TIEs to advance). Rather, each trio will fly away after 10-20 seconds. So you can just move from corner to corner in a clockwise manner to avoid them until they leave. Once these trios are gone, more TIEs using the first pattern will come back for more free kills. But if you do want to kill the trios, I suggest that you briefly fly in the opposite direction for a second or two and then jerk back toward them for a second. This will bait them into a position where you can shoot them with relative ease (just be careful about those torpedoes). If you have R2-D2 and no shields, avoid the trios until he repairs a block or two of shields.
Also, I play console only; I do not play emulators. So a simple laptop screen record would not be useful.
Look guys, I understand that real time video capturing software is pretty easy to get for most of you. But I am poor, 40 years old, and don't really understand this technology anyway. So can I just record my run on my phone and submit that? I just wanna run Quake II Expert Mode on N64, a category that literally nobody has submitted a run for, so I don't think cheating should be a concern.