I had faith my summoning ritual would work!
Blazing Lazers, also known as Gunhed, for the best console of all-time, the PC-Engine.
Jumping from a world of terrible CPC 8bits games, and over the Amiga world of "pretty but not very dynamic" games my friends were taunting me with, it was such a shock.
The opening of the first level Gunhed with its oversped scrolling was just mindblowing. Since that wouldn't be well rendered in a still, I picked a level that traumatized me: the 8th one, with its crazy bubbles being the relentless enemy. The soundtrack was taking a turn for the weird in that level as well. It is all very peculiar.
The game is a Hudson published Compile shoot'em up, i.e. a gem. Probably the best one on a console that is crowded with games of that genre - until Spriggan showed up on CD-ROM (the other Compile shooter of the machine incidently, published by Naxat that time).
Now you are doomed to post something, @divedivedive!
Edit: for those who love videos, the initial moment I was talking about (although it doesn't render all the fluidity of the experience):