I've tried to put these in order from simplest/easiest, to the hardest/longest time to master.
Plus a few tips for them.

Get 200 headshot kills
This is the easiest mastery out of the 3 base weapons, self explanatory, just have a steady aim and ping their heads off.

Get 200 double kills
This requires you to kill 2 birds with one stone 200 times.. aiming for the head will make this a lot easier, but it will still take some time because the zombies are often limping around and don't line up very often for you.. It's best to set up your enemies to 4 players and rinse and repeat checkpoints.

Get 200 ricochet kills
All you have to do is get kills by spraying at something else near them or they can naturally ricochet off of eachother, someone suggested a good way is to spray at a hard stone floor or barrels (good spots in chapter 2:dead ahead) in front of a gathering of zombies. make sure to have Full auto, Drum Magazine, and Damage Mod equipped to make this easier.

Get a kill every 2 seconds for a total of 30 kills
This for me would be the easiest one to master, Just load up Hell Machine, set the enemies to 4 players, and start popping heads off (Make sure you have extended magazine III equipped as this gives you 45 shots instead of 30, just incase you're bad at aiming)

Kill 250 zombies by dismembering limbs
This is quite an easy one to do, it might take a bit longer but as its a heavy shotgun, shooting off limbs won't be hard at all, just get yourself lots of enemies crowded up, make sure you aim at their feet for more guaranteed dismemberment, and you will eventually get this mastery.

Shoot and dismember the legs of 200 zombies
All you have to do is dismember the legs of zombies (using actual bullets and not the melee attachment) Some upgrades can help you with this one, I used Rapid fire bolt III and just sprayed at the FEET of large groups of zombies, This one is more difficult because you're not always guaranteed dismemberment, sometimes you might see a leg fly off but it doesn't count sometimes (at least that's what happened to me) that's why this is one of the harder ones.

Get 200 triple kills or above
This is quite a powerful weapon so it doesn't sound too hard, but getting triple kills isn't that common, so if you want this one just aim for the top half of zombies and hope for the best, It doesn't have to be done all in a row so this will just come with time.

Kill 200 enemies with headshots from at least 50m away
I found this to be the easiest, If you load up the level Hell Machine, the first part where the zombies are coming down the hill out of the smoke is 50m away so you can just rinse and repeat this part of the level until you get it.

Kill 10 snipers through their scopes
It does sound like it's going to be difficult but as long as they're aiming at you, you should be able to get this pretty easy if you just aim for their sniper scope. I wouldn't put this as the easiest as they don't stay in the same place for long, so it could get quite frustrating. 'Hell base Chapter 1', or 'Zombie Zoo Chapter 4' would be good places to try this on.

Kill 100 heavies, officers or screamers by shooting their weak spots
This is definitely the hardest out of the three base weapons purely because this would take a long time (unless you want to reload checkpoints after a gathering of heavies or officers)
screamers are out of the question, it's basically certain death if you're trying to kill one with a sniper.
A good place to get this one is the mission 'Zombie Zoo - Chapter 4 - 4 Player setup' there will be a good number of Necromancers there which count towards this (thanks problemlemon)

100 Dismemberment kills whilst scoring a kill every 4 seconds

Get a kill every 2 seconds for a total of 25 kills

Get a multi kill every 4 secs for a total of 6 multi kills

100 headshots without changing weapons or using melee

Get 7 kills within 1.5 secs of eachother at 20mm distance

Get 20 kills all under 60 secs

Get a kill every 2 secs for a total of 40 kills

Get a dismemberment kill every 4 secs for a total of 60 kills

Get 100 kills without changing weapon or using melee

Get 50 critical hit kills under 7 seconds without changing gun or using melee attacks

Get 10 Multi kills without changing weapon or using melee attacks

Get 50 kills without missing a shot

25 headshots without missing a shot

Get 3 triple kills without missing a shot

Get 25 headshots over 25m without missing a shot

Get 50 headshots with no more than 4 secs apart


Hope this helped a little bit!