I see various websites that claim exceeding 5,000-10,000mSv of radiation would cause death within weeks or even days.
Now say I hypothetically built a ray-gun that shoots radiation beams (any spectrum or type). How many mSv would it need to kill someone instantly?
If you’re gonna claim to be a Supervillain, then you have to allow for the possibility that, in your world, such an exposure to radiation might turn the “victim” into The Amazing Colossal man, or The Incredible Hulk, or something.
Ooh. Hadn’t thought of that. Back to drawing board.
Just get a humongous magnifying glass. Then zap the poor sucker. All the bad rays you need from our friendly Sun!
(Just don’t point it at me…) 
The type of radiation they’re talking about slowly killing people after an initial dose primarily only affects dna and intra-cellular operations.
Exposure kills not by destroying any part of the body, but by massively corrupting the basic functions of most of the cells in that body. The heart will continue to beat, lungs will continue to breath; but blood vessel walls will start falling apart from the strain and red blood cells will start dying off so oxygen can’t be absorbed as easily. The delay is a function of the vast number of cells in the human body, which will NOT be equally damaged by the radiation.
On the other hand, if you wanted to use something like infared or microwave radiation, you could literally bake somebody alive.
Louis Slotin took nine days to succumb to severe neutron radiation exposure.
The problem is that people are not very good at stopping energetic radiation-most radiation will go straight through a person, with only small proportions interacting enough to cause damage. Alpha radiation does not penetrate, but will only damage skin. Beta radiation penetrates somewhat, but does not carry much energy. It does do free radical damage, but that takes time to impact. High energy radiation like Gamma radiation will zip through a body with little absorption and damage. Your best options are LASERS or MASERS, as the human body absorbs light and microwave radiation easily, and it turns to heat which does immediate damage. But it will take a lot of power.
Your only way of killing someone instantly is going to be to cook them, and almost any form of radiation (other than neutrons, gamma rays, or radio above about .1 - 1 m) will work equally well for that purpose, as long as you have enough power. Alpha, beta, protons, light, microwaves, whatever: You’ll need about the same power for any of them. So the question is really just which radiation it’s easiest to get enough power from. On that score, my guess would be masers (coherent microwaves, analogous to lasers).
Or, if you’re playing Space Munchkin, the Laser Laser Maser Bananafannapho Phaser.
I’ve always thought that if you had a fantasy sci-fi world where power was really, really, cheap you could build a pretty damned effective sniper rifle with a maser. Added bonus: you lower it to super-low-power-mode and you get a sniper sight that can effectively see through most common materials. (Think: microwave radar.)
Of course there’s not much point if you have to haul 3 tons of batteries around for each shot.
Strangely, even lethally massive doses of radiation often leave the victim alive and conscious for a brief period. Studies of the proposed neutron bomb found that it would fail to achieve it’s design goal- the immediate, irreversible incapacitation of tank crews- despite enormous radiation dosages.
Plus, there’s the problem that even if you had a narrow beam emitter of radiation, backscatter from the air and the target would subject the source to high dosages of radiation; think shining a flashlight through gelatin.
PSST!
Orbital space mirror.
You didn’t hear that from me!
It would need a cool sound effect - MAZORCH, maybe.
Cecil Kelley took only 35 hours.