Rebel Galaxy

You need a Fault Tracker and any Mining Laser and you can do this on any ship. I tried this on three different ships to be sure; the Tennhausen, the Barracuda, and the Blackgate when actually going for this trophy, and I don't really remember the other four ships names I tried earlier in the game and got my first 15 asteroids with as this is the last trophy I got before the platinum. Smaller ships work best though and I did some basic experiments for this.

Go into a nebula, ice field, some stations, etc were their are ice asteroids or regular asteroids, as these are the space rocks that work the best for this trophy.

Press triangle and then go to pulse, and activate pulse, and find the asteroids that are in squares temporally in those places; those are the rocks you can mine.

Go within 1.4SM near those asteroids and activate the pulse again, a few red circles, generally one to three, will appear on mineable asteroids. Depending on were the asteroid is to you height wise and the asteroid's size, if you are about 1SM away and move your mining laser targeting point near or on the red circle and fire. If you got 2 - 4 objects instead of one you did it right. If you got one, you did it wrong.

To check your progress for this trophy and this I can confirm with 100% certainty of this is that when you pause and go to stats menu, it will say Asteroids Mined and then a number. You can mine a hundred asteroids outside the red circles and or without a Fault Tracker, but only those you mine in those circles with a Fault Tracker will appear in the stats menu for Asteroids Mined. I checked this each time after with the last of 35 asteroids I needed for this trophy, and the number went up till it hit 50 and the trophy popped.

(Note 1: The asteroids don't stop moving, so especially with smaller asteroids it might just be in your interest to ambush the circles with your ship stopped the next time the circle appears.)

(Note 2: sometimes the red circles appear farther away then 1.4SM when you pulse, but this is never guaranteed. I found this more often when asteroids were really bunched up close to each other.)

(Note 3: I got two objects from asteroids mined 7 times and two of them didn't count. I don't know if I was off or for whatever reason it didn't count, so just be wary of that. It won't negatively effect your game, just not count. Any time you do the above steps and got 3 or 4 objects, it always counts toward this trophy.

(Note 4: If you find a large thin cylinder like rock that is typically black and sometimes crystal looking and you you hit with the Mining Laser via the steps above, it was the only asteroid that gave me four objects. They are also generally pretty good objects from them. 8 of the asteroids I mined for the trophy were these types, and five of those times it gave me four objects and generally got all of or a mix of Obtanium, Gold, or Diamonds. If you don't use the Fault Tracker and mine these, you will typically by kinda like a 50/50 ratio either only get one of these nicer objects or one Metallic Ore. So keeping an eye out for those in general is probably worth your time. I generally only find one of these asteroids in there respected asteroids fields/belts. I also found them to be the easiest asteroids to mine with the Fault Tracker.)

(Note 5: You don't need to pick up the objects that come out of the asteroids to get the trophy but it is a resource you can sell. I put a marker on a station with an empty cargo bay and then hit up all the nearby ice fields and nebulas and then go back and sell the stuff at the station and hit a new one after. Depending on the ship your using and cargo space you buy, you may have to do this a few times as using the Fault Tracker right generally nets you three objects from an asteroid and can fill up your cargo bay quickly, but you do need a Tractor Beam to pick up these objects.)

(Note 6: Sometimes the Mining Laser point will move, but a lot of the time it will lock on to the circle and destroy the asteroid. It is best for your ship to not be moving at all when firing the mining laser and when pointing at one of the circles try to be at least 1SM away. Depending on the ship, you need to experiment with the angle of approach generally toward the asteroids. If you too close to the asteroid you'll have a hard time mining in general and more often then not just overheat the Mining Laser for no gains. I found the Barracuda to be the easiest mining ship of those I tried.)

Easy but grindy. Get some Money to buy the Fault Tracker, at least one Mining Laser (a MK1 will do) and, if you don't have one yet, the Tractor Beam. Go to any minefield and use Pulse ( then + ). All the rocks that can be mined will now be marked on the radar. Go to one, use Pulse again and look for the red circles that appear on the surface. Select the Mining Laser and shoot the circles. If you are interested in the kind of loot you will get, just scan the asteroid before going to it (Press Trackpad and scan with ). Get your loot with the Tractor Beam and Bob's your uncle.