Note: Weapon upgrades are cumulative and you do not need to get them in a particular order to "up your guns". All weapon upgrades are out in the open (never in a box) and are usually just hard to find.

Copycat:
An elevated walkway between buildings has this upgrade. High jump to reach it.

Dead Men Walking:
There is a weapon upgrade near one of the two bonus mission crates (the ones that explode).

La Famiglia:
On top of the mansion. Atttempt it after disabling all the guns and using the greenhouse on the left side of the mansion as a step-up.

Under The Gun:
Near the multi-tier parking structure where the Predator started the misson. Use the destroyed floors to reach it.

The Machine Men:
On the track past where the Machine Men initially started off.

Monster Squad:
On the west side of the map, there was one of the lift power boxes inside a small tunnel (on the ground) in the previous stage. The weapon upgrade is in the fire.

Rescue:
There are four upgrades here. If you attempt to do the bonus mission here, you wind up opening all the doors and having acccess to all the bonus upgrades and missions.

Ten Thousand Ways to Die:
There is a weapon upgrade on the side of one of the final buildings (you will be able to see it but cannot reach it (forcefield) until you defeat the upgraded battle armor.

Hot Time/Old Town:
On top of the church. use gecko ability to reach it. If It Bleeds: At the 1-2-3-4 junction where the power core is, the weapon upgrade is on the lower level, where the mines are.

In The Flesh:
The upgrade is at the end of one of the very narrow bridges at the edge of the arena.