Aliens: Fireteam Elite

The fastest way i have found to do this os to play horde mode on standard. Make it to round 20 then go back to base. You should get about 28 thousand and change for XP. You dont have to use that gun you are working on because the class and the guns all get equal XP even if the gun doesnt get used. Also you only get like 4 thousand XP after round 20.... iE: round 30..40..50..and so on. Just go to 20 and stop and rinse and repeat.

EDIT: The only way faster than the above solution is play minimum 2.0 experience on the first stage. I say the first stage cause your can do it in 20 minutes or faster. I try to minimum with a buddy at 2.25 but when we run out the 2.0 is next in line.

Simply get 30 weapons to four stars. If you have less than 30 weapons, look for hidden caches and complete missions on higher difficulties to unlock more weapons.

Use challenge cards that grant extra experience to speed up leveling. Playing solo I did the grind on casual difficulty while I worked on getting synth and elite kills with cards like Lonely Perfection, Game Over, Man, High Tempo Operation (all 1.5x), and Slow But Sure (1.75x). Doing the first level is easy with harder challenges that grant more than 2x experience (No HUD, Adrenaline Junkie, Coming Out of the Damn Walls).

When the game released, all weapons accidentally had fully leveled stats, so in the first patch the devs said "oops" and leveled up all unlocked weapons to four stars, making this achievement unobtainable until the following update. So if you had quit the game in frustration during this time, it works now and you've been saved a LOT of grinding.

Tracking is still broken. At 29 four-star weapons I was tracked at 23%. The achievement popped at 30 weapons however.