Rebel Galaxy

Faces of Gozu, Progenitor Shards and Antimatter Specks are rare commodities. It's possible to mine them but it's incredibly rare to find the right asteroid field, much less have the right mineral inside the asteroids. It's possible to find merchants carrying them if you scan them, but you'll need to pirate it off them to get it. There is also a pirate mission (if you follow the pirate line of side story missions) that gives you a speck to haul but it's currently unknown if that one counts for the trophy. The easiest way is to play the story and fight the enemy then eventually they will drop as loot. You can also wait for Convoys or Science Vessels, particularly when Archaeological events occur, then rob the ships.

The story introduces an alien race called the Viriax. Larger Viriax ships like their Dreadnaughts may drop them as loot and this is one of the better ways to get faces, specks and shards. Fighting Viriax Dreadnaughts, you're quite likely to get a drop.

If you do intend to go the mining route, then you need to find a special asteroid field where the asteroids are extremely large compared to even the largest ships but these can be found randomly in any system. Once you find these asteroids, you can tell that they are the special asteroids. Not only are they huge, they take upwards of 2 minutes to break, unlike normal ones which break in seconds.

Here's a picture of one of these asteroids, note the size of it, compared to the Radovich Heavy Hauler:



Unfortunately finding these fields is a matter of pure luck so you have to keep flying and hunting asteroid fields. You can accelerate this a bit by using the zoom in your system map. Find a colour patch which indicates a field and zoom in to see if you spot one of these asteroids. If not, then zoom out and find another patch. Even if you find such an asteroid field, chances are these asteroids will yield Faces of Gozu but only rarely will you get Specks and Shards.