40 seconds or so not counting prep time. I had more, but the shots didn't turn out well.
Here's the exact build I used:
I'll post the bullets in the GE2 bullets page, but the gist is that you use activate the 90%, 30% (might be 20%, I can't remember), and 70% BR vows, as well as the one requiring a part break (結合崩壊), which gives you a 924% total modifier. Use the first of the two bullets to hit the Crimson Orochi from a distance — it should deal ~45k damage, break a part, and trigger BR instantly. Hit it with as many long-range shots as you can, then switch to the second bullet (short-range variant) and blast away at it when it gets close as fast as you can. Each hit will deal anywhere from 15 to 25 thousand damage.
Happy hunting!