So, 85% of life is going to be wiped out, and humanity's goal is to be in the 15%?
This is a tough ask. I'm not sure exactly what you mean by "stripping the atmosphere", but if literally all of it is removed then (a) the seas boil due to lack of pressure and therefore (b) I don't think anything like as much as 15% of life survives. So it's not quite that bad. There's some atmospheric pressure left, at least enough to keep some parts of the ocean intact.
But let's face it, the surviving 15% is going to be tiny little stuff that lives in water, not great big vertebrates who live on the surface, sunburn easily, and need to breathe air.
Best bet is to build a sealed bubble underground to support a small number of survivors, but while that's within our technology it's not really within our expertise. The closest is Cold War nuclear bunkers, which might be good enough to survive the event, but didn't really anticipate a thousands-of-years aftermath in which the land remains inhospitable until we somehow re-seed it.
Frankly for an 85% extinction event I'd put my affairs in order and wait for the inevitable. But the best chance is to try to invent a self-sufficient bunker before it hits. The more we know about how long it'll be until the atmosphere is breathable again (if ever), the better. The longer we have, and the shorter the Era of Death, the more chance of developing technology to make it work. Given a long enough horizon, we could be bio-engineering radiation-resistant cyanobacteria and seeding the oceans with them, with the intention of oxygenating the new atmosphere ASAP so that we can emerge blinking into the light after a few thousand years to start planting our seeds.