I got this information from this steamcommunity post by Masquerine.

I recorded what weapons I found per mission, per difficulty. Most weapons seem to have multiple places they can be found. It is possible I may have missed possible drop locations, but you can find all the possible weapons listed here for 100%.

Easy Difficulty

Mission 1: E1 Plasma Launcher, LAZR-197, Rapier Thrust, Proto Thunder Sniper

Mission 2: E1 Plasma Launcher, LAZR-197, Mirage Zero, Proto Thunder Sniper

Mission 3: Dual Plasma Launcher, E1 Plasma Launcher, LAZR-197, Mirage Zero

Mission 4: LAZR-197, Mirage Zero, Proto Thunder Sniper

Mission 5: E1 Plasma Launcher, Mirage Zero, Proto Thunder Sniper

Mission 6: E1 Plasma Launcher, Geist, Mirage Zero, Proto Thunder Sniper

Normal Difficulty

Mission 1: Mirage Zero, Rapier Thrust, Thunder Sniper A

Mission 2: Dual Plasma Launcher, Ixion 2-Way, Mirage Zero, Rapier Thrust, Thunder Sniper A

Mission 3: Dual Plasma Launcher, LARG-V, LAZR-197, Thunder Sniper B

Mission 4: M2 Rapier, LARG-V, Thunder Sniper B

Mission 5: D Plasma Launcher, E1 Plasma Launcher, Mirage 5-Way

Mission 6: Ixion Wide, LAZR-199, Mirage 5-Way, Proto Thunder Sniper

Hard Difficulty

Mission 1: LARG-V, LAZR-197, LAZR-199

Mission 2: LAZR-197, LAZR-200, Thunder Sniper C

Mission 3: E1 Plasma Launcher, 3x Plasma Launcher, Rapid Mirage

Mission 4: Rapid Mirage, Thunder Bow 15, Thunder Bow 20

Mission 5: D2 Plasma Launcher, Mirage 5-Way B, Plasma Whip, Thunder Bow 20

Mission 6: D2 Plasma Launcher, Ixion 3-Way, Mirage 5-Way B, Mirage 5-Way S

Hardest Difficulty

Mission 1: LARG-W3, Mirage 5-Way B, 2x Plasma Launcher

Mission 2: Ixion 3-Way, LARG-W3, LAZR-201, Plasma Launcher R

Mission 3: LAZR-201, Mirage Rumble, Proto Thunder Sniper

Mission 4: D2 Plasma Launcher, Mirage Rumble, Plasma Whip S

Mission 5: Ixion 5-Way, Plasma Whip S, Thunder Sniper 40

Mission 6: Cyclone Laser, Ixion 5-Way, Rapier Thrust, Thunder Sniper 40, 2x Plasma Launcher S

Inferno Difficulty

Mission 1: Ixion Mark III, MX Rapier, Rapier G Thrust, Thunder Sniper 40

Mission 2: E1 Plasma Launcher, Geist D, Ixion Mark III, Rapier G Thrust

Mission 3: Ixion Mark III, Fenrir, Thunder Bow 30

Mission 4: Fenrir, Plasma Sweeper, Thunder Bow 30

Mission 5: Ixion 4-Way, LAZR-201, LAZR-300, Plasma Sweeper

Mission 6: ARC-LAZR, LAZR-300, Plasma Sweeper, Rapier Thrust, XSX Plasma Launcher

Hell Difficulty

Mission 1: Ixion 2-Way, Ixion 5-Way, Ixion 6-Way

Mission 2: LAZR-197, Master Rapier, MIrage Zero, Proto Thunder Sniper

Mission 3: Fenrir, RZR Plasma Launcher

Mission 4: Ixion 2-Way, Ixion 5-Way, Ixion Mark III, Thunder Bow XD

Mission 5: Fenrir 3-Way, MX Rapier, M2 Rapier, M3 Rapier Thrust

Mission 6: Ixion 9-Way, SIG-LAZR, 3x Plasma Launcher