I think that this is excellent work so far, but I do have a couple of suggestions.
The point from which the phasers are being fired could use some kind of light flare to cover the sudden thickness of the beam, or maybe you could taper the beam at that end so that it doesn't seem to jump out like that.
If you look at the phaser fire in
TWOK, the beams are tapered at both ends, and cast a definite glow on the hull as they're fired. I'm not sure how that might be done, but I would imagine that others here who are more skilled than I could tell you how.
Alternatively, you could just add a light flare at the firing point like in
First Contact. That might be more simply done, and it would look good.
Also, if you can brighten the point at which the shields are being hit so that it actually obscures the weapons hitting it, and have it gradually fade (with a particle effect, ideally), that would look incredible.