Update 19.5 Shotgun Weapons List
Weapons in brackets are Variations on that Shotgun, so there is a Strun, Strun Mk-1 and a Strun Wraith.
• Boar (Prime)
• Hek (Vaykor)
• Strun (MK1, Wraith)
• Tigris (Sancti)
Mk.1 Weapons you can buy for Credits from the Marketplace and provide quick replacements.
Lot's of weapons require a Mastery Rank, but by leveling weapons you increase your Rank so this shouldn't be a problem, just make sure to Rank up regularly.
Prime Weapons require Void completion, often high level Survival/Defense 'Rotation C' drops. These are endgame. I use Primarch Prime Part Guide
Lots of weapons like Prisma, Vandal and Wraith Weapons are Limited Time exclusive weapons, some re-appear as Sortie or Week/end event rewards but some are gone, maybe for good. (Dex are Birthday weapons and they pop up once a year around April for free)
Anything else with an interesting alternate is probably a high level Syndicate Reward and requires MR12.
All in all, most are endgame weapons if you're just starting and want to finish off Shotguns, then just stick with the vanilla versions, buy the Strun Mk-1 and then make another weapon, the Drakgoon was interesting as it charges like a Bow and is powerful.Check here for required Mastery Ranks
or the Marketplace.
.Leveling weapons to Rank 30
The best way to level weapons is to play Survival or Defense missions and kill lots of enemies, then extract for the bonus exp, you'll get lots of weapon mastery whilst unlocking all worlds, doing alerts, unlocking other achievements and just playing the game. Remember to always swap for you next weapon and have one ready to swap.
Lots of Dark Sectors have Affinity bonus (+Shotgun), use a Warframe that supports you but doesn't really kill enemies so you rely on your weapons, being in a group spawns more enemies for more exp.
Elara on Jupiter is a great mission for Affinity, as the anti-moas spawn early and often, and they give a fair amount of affinity around 7-9x the exp of grunts.