This achievement can be missed.
Once you start the second phase you play in a different area altogether (This can only be done in the 2nd phase of the game; don’t start the 3rd phase before you get the achievement as you’ll change areas and you’ll be forced to start a new campaign and reach the 2nd phase again). As a result, you get access to a black hole. Sooner or later you’ll get a mission that brings you right next to it – you’ll get a pop-up the first time so you’ll know when you’re close enough to attempt this.
Keep in mind that there is no way to save the ship/crew once you’re next to it so unless you’re prepared to lose them and start from scratch, I advise you to save scum or do this on a different campaign. The fact that you get access to it in the middle of the game makes this achievement a nuisance.
Despite the achievement icon, you actually need to send the ship itself inside the black hole (no matter how many crew members are on board – if you use the escape pods they’ll end up in the black hole; do this in a different area if you want to try to save part of your crew). Once you reach the black hole move your commander from the command post. Engines will stop and you’ll get sucked in. A timer will start and once it ends there’s no way to stop your ship’s demise. The achievement will pop up momentarily.