Find the following unique weapons by searching the corresponding locations:
In mission 10, during the objective to destroy the third AA gun, find a container with a rocket launcher inside. Search that container further to find the flamethrower.
In mission 4, while exploring the tunnels with O'Neal you will be stopped by a door that must be sliced open. Leave O'Neal waiting beside the door and follow the path to the left of him. There is a table with the pistol at the base of some steps.
In mission 1, explore the gravity well with O'Neal and reach the top floor, where several aliens will attack. Kill them then search the nearby rooms and catch up with O'Neal. After you are reunited,defend O'Neal from alien attacks while the door is opened. Searcg the side rooms on this floor to find armor and the shotgun.
Hudson's pulse rifle
In mission 5, find the elevator, ride it up to meet with O'Neal, and get your weapons again. On this floor, search the offices to find the pulse rifle.
In mission 9, turn left as you enter the interior of Hadley's Hope. Search the path until finding a room that contains armor and the pistol.
Vasquez's smart gun
In mission 6, you will enter an area full of shipping containers while on your way outside with O'Neal and Bella. Fight through the soldiers then go down the stairs to a garage where aliens and soldiers will enter through the open doors. Clear them out, then search the pallets stacked against the wall to find the smart gun.