The Gold Desert Eagle is a new weapon introduced in contracts, and 1 of them can be found during a few missions. These are singular, however and you cannot simply find 2 for this achievement, you must find the specific 'Dual Gold Desert Eagles'. You will find the dual gold desert eagles during the mission 'Asylum Aftermath', but first you need to acquire a key card on the ninth mission 'The Wang Fou Incident', which can be found on Lee Hong's desk.
To get the key card, you need to travel to the mansion, but there is no map of the mansion or the sewer, so you will need to try and remember the way from using the maps in the second to last mission 'The Lee Hong Assassination', which is in the same area and has all of the maps. You need to make your way to the elevator in the restaurant which will take you to the sewers. Then you need to navigate the sewers, to the other end where there will be another elevator, that will take you to the mansion. When in the mansion, you need to find the staircase that leads up to the second floor and to where Lee Hong's office is.
After acquiring the key card, you need to return to the mission 'Asylum Aftermath' and you will need to find your way to a cryo lab. The best way to find this is to follow the green escape route on the map, then when you reach a passageway with a short staircase, you will find the lab at the bottom of these stairs. The dual gold desert eagles are just behind the door, that you need the key card to unlock.