Can't Touch This

Question: How would you model Achilles' invulnerability, or invulnerability like it? A trait like that used by the Hydra and the Gorgons in Demigod? Baldur's unique Stamina Knack 'Unkillable' from Ragnarok? 'Mere' high Epic Stamina? Or another solution?

It really depends on what you want as a Storyteller and how you intend for Achilles (or whomever) to appear in your games. A number of different approaches are possible, but each one is good for different things.

If you actually want Achilles to be invulnerable, decide what that means to you - does it mean he can't be injured? Does it mean he can be injured but not knocked out? Does it mean he can be knocked out but not killed? Once you know that, if you're not planning for him to fight any PCs, your work is pretty much done; the excellent Storyteller tool of Fate will do the rest for you. You're telling the story, after all; Achilles isn't going to get hit, hurt, or distracted by anything unless you weave that into the story, so simply don't include that. If things are happening around him, just narrate what he's doing as if he were the hero of an action film - bullets fly every which way, enemies always get taken out before they can touch him, and so forth. The players will get the impression of his badassery and you don't have to worry about fiddly things like mechanics at all. This is actually also what we do with a lot of the Aesir gods - Thor can't die before Ragnarok, after all, because he's scheduled to die then, so unless someone pulls off some insanely crazy stunts that manage to flout Fate itself, he pretty much gets a pass when he goes out to stomp around and bust heads.

I'm actually not at all fond of the idea of giving people unique "I can't be killed!" knacks, for a lot of reasons. The first is just that it's weird and out of line with everything else in the setting. The second is that it prevents PCs from being able to do anything whatsoever to deal with it - sure, Thor probably isn't going to die before Ragnarok, but if a group of PCs decided to hate him and pulled off some truly insane, Fate-defying feats in an attempt to seal his doom, having their efforts invalidated by a flat, incontrovertible knack would be super lame. The third is that I've never seen a situation wherein it was necessary - its only purpose is to give the ST an easy out to prevent anyone from killing an NPC, but if you're the ST, you can already keep any NPC alive that you want. Give them Rainbow Bridge. Give them Deus Ex Machina. Have some other NPC come save them. Nobody needs a weird extra knack to illustrate that they aren't going to get killed - if the plot says they aren't going to get killed, the ST should find a (politique, sense-making, non-player-cockblocking) way to see that they keep ticking.

Also, in Baldur's case it's always seemed a bit weird, anyway - Baldur doesn't have better Stamina than everyone else, after all, he just has the knowledge that his mother went around and did some voodoo to keep anything from hurting him. His story is actually the inspiration behind our invention of the Entreat Immunity boon, which basically does exactly what Frigg probably did for him but on a smaller scale. If he actually had uniquely awesome Epic Stamina, he probably wouldn't get immediately taken down by the first wound he ever sustains in his life.

So really, unless you plan for this indestructible NPC to actually fight the PCs, you have no reason whatsoever to have any mechanical model for what makes him indestructible at all. As the ST, you have unlimited options for keeping him alive, and your players don't need to know the mechanical details of how Achilles is invulnerable, since their characters certainly aren't going to be privy to that information.

If you are, however, planning for your PCs to fight Achilles (or preparing in case they decide to do so on their own), you do have a more difficult situation. Again, this goes back to what you, as the ST, want Achilles' invulnerability to look like - you might rule that PCs wound him countless times but he keeps on going, or that their attacks bounce off, or just that he seems to be extraordinarily lucky and they can't get a shot to hit him without something interfering. The only part of Achilles you need to worry about is his heel - that's the only place the PCs are going to be doing anything to him, right? And unless they're extremely stupid PCs or have never heard of classical literature, they're going to know it, too, so figure out what kind of difficulty they need to meet to get him where it counts, and don't sweat the behind-the-scenes, unimportant details of all the things that don't count.

John suggests, on his way out the door to rehearsal, that the easiest way to do it is just to declare that Achilles' skin is now a star-level relic with hundreds of soak, so that they can hit him all they want but are probably not going to have any chance of injuring him. If you'd really like a mechanical basis, that's short, sweet, and also might help clue in PCs if they happen to take a look at him through the Unlidded Eye.

Most of this post was about Achilles because he's the easiest example, but the idea really applies to any indestructible (as decided by the Storyteller) NPC or being in the game. If it suits the story's purpose for him to be indestructible and the PCs have no chance of getting around it, it doesn't really matter what mechanical justification you want to give for it (and beware - players can be very crafty, so if you do give a mechanic, there's always a chance they can find a sneaky way around it!). If the PCs can destroy him if they try hard enough, focus on how they'd have to go about doing it and what they'd need to succeed. Everything else is gravy, and gravy the PCs and players will never even need to know about at that. Whatever makes most sense to you and fits the character in question is the best solution. (That said, though, I'd also use truly invulnerable characters extremely sparingly - neither enemies the PCs can't hope to defeat nor friends they can't hope to measure up to are fun for them for long.)

Incidentally, Achilles has appeared in our games as a guest star. The PCs did not attempt to destroy him, partly because they convinced him to go do what they wanted him to do in the first place (fight Agamemnon) and partly because at some point they noticed that he was actually missing his heel entirely and got pretty spooked. (Also, I'm fairly certain Aurora might have had the tiniest little crush on him after he gallantly caught her when her prophecy of his success knocked her over.)

Addendum: It occurs to me that you might be asking this question because you suspect there's a chance that PCs might throw themselves into the Styx in an attempt to gain the same kind of invulnerability Achilles has themselves. In that case, I'd totally let them if they can get there and have the stones to do it, and I'd probably give them giant bonuses to their soaks and/or Stamina rolls - but considering that everybody doesn't go take a quick dip in the Styx, I'd probably also suggest slapping them with some negative consequences as well to explain why. Maybe they suddenly gain five dots of Malice (since the word "styx" can also mean "hatred") or find themselves having lost some of their mental or social stats to make up for their newfound excellence in the physical arena.