I'm in the middle of doing a similar thing but not Damascus, just getting gold for my favourite weapons.
The worst for me are the mounted kills and crouch kills, the rest are pretty straight forward.
The only guns I have yet to rank up are a couple of shottys, the 680 and the 725. The 725 is brutal with the sawed off barrel and sawed off stock and fair play the opposition give me plenty of abuse for using it lol
Once you have done the Riot shield and launchers everything thing else feels easy.
Quickest way I've found to gold any gun is to do it systematically.
For a new unlevel gun.
1. Use Double XP took to level the gun asap to max to unlock all the camo challenges.
2. Play Shipment, or Hardcore Shipment depending on the gun e.g. pistols, some smgs, etc
3. The first camo challenges you unlock are crouching kills, headshots, hip fire. You can generally do these together quite easily on shipment, use a merc foregrip and laser for better hipfire.
4. Once you get the Longshots and Mounted kills challenge play Hardcore Shoothouse, mount the wall that runs through the middle of the map. Equip a 3x optic with a balance between range and ADS so that you can mount as quick as possible and play hardcore so you should be able to 1 shot kill anyone to the head no matter the gun.
5. Once you unlock the no attachment challenge, switch to doing this immediately as you will general do other challenges along the way.
6. You should naturally get double kills and 5 attachment kills, however 3 kills without dying and headshots might take a bit longer depending on your skill level and the gun.
Once you get into the flow of it a SMG, pistol, shotgun should only take around 3 hours to complete. AR, LMG and Snipers around 4-5 hours. Launchers and Riot shield god knows :<