Vanquish

Throughout the game, you'll come across green crates with "Marines" written on it. Approach one of these crates and press to reveal the (random) weapon it contains, then press to pick it up. There are also grey metal drop pods where you can get weapons from. Unlike the crates, these drop pods have no random weapons. Once you find a drop pod with an Assault Rifle, that same drop pod will always have an Assault Rifle. Also, when you revive a teammate, he'll drop a random weapon as well. So do enemies on occasion.

As you'll probably remember from the tutorial, picking up the same weapon you're already carrying, will upgrade that weapon gradually if the ammo for that weapon is at full capacity.

Sometimes, enemies can drop an "Upgrade" item instead of a weapon. This will upgrade the weapon you're actually using in combat by a full rank (1 star). So, before picking up this upgrade, be sure to select the weapon you wish to upgrade by selecting it using the D-pad. Some weapons will be fully upgraded with 6 stars (grenades, rocket launcher), other weapons will be fully upgraded with 11 stars (assault rifle, heavy machine gun). You'll know that a weapon is fully upgraded as it'll show you a symbol (eagle with three stars) below that weapon in the bottom right of your screen.

You should get this achievement way before the end of the game. Just open every crate you come across and pick up every weapon especially if you're already carrying it.

But if you're in a hurry, a quick and easy way to get this achievement, is on Act 1-3 (Giant). On the part of the level where you have to defeat KNRB-0 Argus, there are approx. 8 weapons to pick up. Pick them up, let yourself get killed, choose "checkpoint", rinse and repeat. Note that doing it this way, you will miss the "Living Legend" achievement. Refer to that achievement's description for more information.