As stated, this achievement is based purely on chance and luck. So there is no skill involved, or any right or wrong way to get the achievement. Simply play it, and overtime it will unlock. You can see Calex dEUS and Maxxxxine's solutions for tips and advice on this matter.
What I can offer instead is the probability of you rolling 4 Targets on a dice roll.
I rolled 71 dices over the course of an evening before I got utterly bored of notating my results. But here is what they are:
Dice 1: 22 targets
Dice 2: 29 targets
Dice 3: 28 targets
Dice 4: 32 targets
So the average is 27.75 targets rolled ( (22+29+28+32)/4 ) on a given dice.
Dividing 27.75 into 71 dice rolls yields a 39.08% probability of rolling a target on a single dice. I doubt Id software coded this number, so I am going to round up to 40% which seems more feasible. In essence, think of a five sided dice where 3 of the faces are skulls and two which are targets (since the mini game is with holograms and what not, I don't see this as being too farfetched).
So to roll one dice as a Target is 40%, or 2/5.
To roll two dice as Targets is 16%, or 4/25 (2/5 * 2/5)
To roll three dice as Targets 6.4%, or 8/125 (2/5 * 2/5 * 2/5)
To roll all four dice as targets is 2.56%, or 16/625 (2/5 * 2/5 * 2/5 * 2/5)
So overall you have a 2.56% chance of getting all Targets on a dice throw.
Not very encouraging!
(hope that math is right, it's been a while since I took that stat class back in college)