Alright, here’s a question, as I don’t know how to do so. 

My players are about to infiltrate a giant castle for some (unkown to them) legendary magic items, which they have been told will end the universe as they know it. I have put a big emphasis on on that they should be stealthy, but I have a few questions before I do this.

1. How do I encourage them to sneak? We have a barbarian with a bloodlust, and some people who (from recent events) aren’t very stealthy in nature. 

2. How do they not die? I’d like to fill this place with powerful people (this is supposed to be a cult castle), but I don’t want them to die because they roll a natural 1 on stealth. Any suggestions?

Please help, and thank you.

One way to go is to make the risk of being caught not 'death', but 'immediate failure of the mission'. So what if they are aware that the bad guy knows someone might be coming for the artifact--and the bad guy is ready to bail at the first sign of trouble. Bad guy has a teleport/dimension door ability, and if any guards start yelling, if the sounds of combat are heard, the bad guy is gone. And with him, their chance to snag the artifact.

That way, you don't need super lethal guards, you just need guards who can yell as they die :) If the players know the bad guy can quickly escape, they'll know they have to get to the artifact without causing anyone to yell. 

Also, how about letting them spend some time planning and prepping, like the planning montage from a heist movie?  They could work together to make useful rolls and build up a "stealth bonus" that can be applied to all Stealth rolls during their infiltration, it could be a +5, it could be simple Advantage or it could be something that excludes Critical Failure (if that is something that your game uses).

The prep session could be quite good fun as the players roll for their PCs to secure loose items, plan a route, camouflage themselves etc, etc ...

I like the preparation idea, that sort ofactivity would require planning and the mechanical bonus will encourage that, on top of the options listed you could also give them X opportunities to reroll bad dice, more planning means they get more rerolls to avoid things going wrong. Another non lethal failure would be the party get captured, or rather than teleporting away the big bad has a safe room (magical and/or mundane), so if there is an alarm retrieval will be much more difficult and require rethinking.

If you want to keep them in stealth mode at the risk of making the task a touch easier--but possibly more fun--you could use a mechanic similar to what the Leverage RPG uses--the 'flashback'. 

The idea is that, when a character is in a tricky situation, they or someone else can make a roll to say "Ah, but remember when I..." and retcon something to help. For example: Fred is alone, trying to sneak into the Gate House to steal the key to the dungeon while the rest of the party waits in the garden. Fred is hidden in the bushes outside the gate house, but a guard just rolled a high perception roll and is going to notice Fred. Susan says "Wait, but remember when I had my invisible familiar follow Fred? The familiar knocks a vase over at the end of the hallway to distract the guard." Susan makes a roll, and if successful, that's now what actually happened :)

It's a fun mechanic. You just have to not contradict anything that has actually happened--Susan couldn't have ordered her familiar to do something else earlier and now change her mind, but if she hadn't had her familiar doing anything at all, she can say that she did. You can do this by assigning a set number of 'plot points' per player--spend one to do a flashback, no more than 1 flashback per situation.

And to steal from another game, it can be fun with things like this to set the DC for these by appealing to the rest of the players. Susan spends a plot point in a situation and says "Wait wait, remember when I...". When she's described the flashback in detail, you can have everyone at the table write down what they think the DC should be, based on things like plausibility of it working, but also cool factor. Then a roll for whatever is appropriate.

Or...not even roll at all. Just give plot points, they spend them as they wish, but you as the DM keep your NPCs reacting and challenging the PCs. Leverage is a 'Heist' game, so this kind of mechanic is perfect for a 'sneak in and steal the thing' heist mission :)

another option is to make stealth checks less all of nothing. compare it to combat where 1 shit roll means nothing good happens, something bad happens and/or valuable resources are spend, but it doesn't mean that combat is immediately lost. stealth could work the same. a player walks up the stairs but rolls bad for their stealth, instead of being seen this could result in the stairs creaking horribly, alerting people that someone is walking up the stairs. what do they do? pretend they belong? try to find cover to disappear into? create a distraction? all run a different direction forcing guards to split up and then try to shake them? turn that failure from a fail into a moment of potential problems that your players get to solve.

(yes, i know this post was from 2 years ago, but i found it while looking for more help with planning stealth missions so someone else may too)

Why are you trying to force them to do it as a stealth mission? They're the players; you are the DM. You put the challenge in front of them. They decide what to do about it. 

I submit that you should not make only one solution to a problem in your campaign. Rather, create the obstacle, tell them what the conditions are to the extent that is appropriate for their characters to know. And let them decide if they want to be stealthy, make a frontal assault, etc. Surely if they learn that they would be outnumbered 25 to 1 or something, they would be smart enough not to try and just bash the door down - even the barbarian can't be that stupid.

I highly recommend that, instead of trying to make them to stealth and setting it up so that if they roll badly on the dice they all die, you should create an interesting base for the villains with lots of individual obstacles, the potential for alarms to be raised (or prevented from being raised), and so forth. Guards in guard rooms. Patrol schedules around the battlements. Sleeping shifts for the cultists. Hours of religious worship when they are all (but a few) in the cult's chapel. Create a "day in the life" schedule for your castle and give the players whatever appropriate information their characters would have. Then, it's up to them what they do to try and infiltrate. 

For example, maybe they won't use stealth. Maybe, instead, they'll use polymorph and/or disguise self to make themselves look like cultists and try to deceive their way inside, rather than sneak. Why would that not be an acceptable option? Maybe they will set up a diversion or a decoy situation at a side door. The two guards get distracted by something, and when they go to look, the characters sneak in, maybe no stealth is needed. Maybe they will think of something that would never occur to either me or you.

Give them the freedom to do these things, instead of trying to convince them to come up with the one solution you have pre-determined.

It's perfectly fine as a DM to build a challenge and to envision how you think they will probably overcome things. In fact, I'd argue it's probably your responsibility, to come up with at least one way it is possible for the PCs to succeed (if they happen to think of it). But your players will often think of something totally different and if they want to try it, let them. By all means, find a way to warn them that a direct frontal assault is out of the question, but that should be easy to make obvious. For instance, as they approach the stronghold but while they are still too far away to be spotted, they see a detachment of 40 troops on horseback and with lances riding into it over the drawbridge. That should let them know there are a lot of bad guys in here and it would be suicide to just attack from the front. After that, leave it up to them to scout the layout, and come up with their own plan.

Nat 20 on your roll to utterly ignore the entire point of the post I just made. 

The spell's powers are utterly irrelevant to my point, which is there are any number of ways someone could assail a heavily armed base, and stealth is only one of them, and the DM should not insist that the party use one and only one way to solve problems (namely, "the DM's way").