Hello Flygon! I believe nobody has recorded any movies of this game yet.
Generally, autoscrollers are not good games for TASing and Battle Squadron feels somehow slow (at least in the beginning). However, this game allows 2 players to play simultaneously, which might be interesting to see. Also, interestingly, difficulty is set by changing the speed of enemy bullets (this should be set to the maximum value: 400). Who knows, the 2 player mode might be cool, if it's done well. You might want to see examples of other autoscroller movies (like Gradius) to get ideas for your attempt.
I have not played the game much myself, so I can't give any detailed hints, but it seems that the game has some alternative route possibilities(?), so the fastest and shortest (or maybe the most interesting/entertaining?) routes should be used.
By the way, your signature is nice, but the size (and image-like nature) of it is against the rules here. :)
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Edit:
Heh, they use foreground elements to hide enemies and have some backgrounds colored to correspond enemy projectiles. Quite nasty gameplay development...