How to get the Rat King in Destiny 2:

Complete the main story and get to level 20 - this unlocks the Enemy of my Enemy quest on Titan.
Complete the quest Enemy of my Enemy - it's a blue quest marker you'll find in the world and on your map, which ends in you being given the option to kill or save an enemy captain. Either way, when you complete it, you'll get the Rat King's Crew item. The item takes up a Kinetic Weapon slot, but can't be used as one.
On the Rat King's Crew you'll find a strange riddle. This is, in fact, the first of four riddles, and you'll need to solve them, and then complete their respective tasks, one at a time to get the weapon itself. Read on for detailed solutions to these in the section below!




Rat King riddle solutions:

"The Rat King's Crew runs to and fro, good girls and boys know where to go, pick up your toys and daron your socks, on errands of woe, on errands we walk" - Complete two Patrol Missions with a Fireteam of at least one other Guardian - to do this, you need to complete the Patrol quest, granted by Cayde in the EDZ after you've finished the main story questline. Then, any two Patrol Missions will do, as long as there's at least one other Guardian in your Fireteam.
"The Rat King's Crew goes arm in arm, to fight as one, to do no harm, so have your fun and run outside, rally the flag and we'll never die" - Complete two Public Events with a Fireteam of at least one other Guardian - this is one of the simplest steps. Simply head to any Public Event with a Fireteam and crack on.
"The Rat King's Crew goes four and four, with good good fights they learn to score, then three as one they stand upright, return from past the wall and wanting more" - Complete two Crucible matches with a Fireteam of at least one other Guardian - again, dead simple. Head to the Crucible with your Fireteam and crack on! Both Quickplay and Competitive will work.
"The Rat King's Crew stands three as one, they see Night's fall and fear it none, but watch the clock as you scale the wall, lest five remain hope comes for none" - Complete the Nightfall Strike with at least five minutes remaining - and here's where it gets tough. This is taking most players several tries, because having at least five minutes remaining on the clock, even though you can stall its progress, is no easy feat. Our advice is to have damage of all three types - Void, Arc, and Solar - available in your squad, and ideally within your own personal build, because the 'burn' affect, boosting damage output of that element, rotates periodically in the Strike. Have a plan before you set out, run past enemies you don't need to kill to progress, and try to get your Power Level as high as possible in advance!

The Rat King's Crew will pop up on the right each time you complete one of its steps,and likewise soon as you finish that final step of completing the Nightfall with at least five minutes remaining, it'll instantly become available as the Rat King Exotic sidearm.

And with that, you're done! Enjoy lording over your fellow Rat Pack subjects, your majesty!