After completing a few new rounds of investigations for Prophecy, you'll be given a morality choice by 3 inquisitors aboard your inquisitor ship.
*** Spoiler - click to reveal ***The radical option is to let the Alpha Pariah go murder Fabius Bile's clone first, while the Puritan option is to send her straight into the warpsurge.
It would seem that regardless of which you choose, you'll end up going on the mission to hunt down the Bile clone. This will involve a multi-stage boss fight. If you've already done the Eye of Terror achievement, you can play on Story Mode and the boss will just melt. Especially with a bunch of the Mechanicus' constructs.
Win that fight, and you'll automatically get a scene where the Alpha Pariah departs aboard the Martyr.
Once you're back in control aboard your inquisitor ship, speak to Captain van Wynter to wrap up the investigation. Credits will scroll, and the achievement will pop after a couple of moments.