I believe it needs the head, the majority of the torso and most importantly, the heart. I think some older editions were more specific, 5th is not really beyond the head and heart, so really you only need as many parts as they made robocop with.
Which would actually be pretty cool, in order to res a person you needed their head and their heart, but still needed a full body, so you could res someone in someone else's body, just with their head and heart.
This seems like a bit more of a campaign-specific twist than I'm aware of. That is, in 3e (and I'm
fairly sure 4e too) it's just some important body part, but it might be the head (or skull, if it's decayed) specifically. I've never heard a mention of
needing the heart before.
That said, though? This could be a pretty interesting premise in a campaign where death was not unusual. "You can accept death...or you can accept a new body." Presumably that would mean (a) rerolling your stats and (b) possibly taking a Charisma hit. Sort of a campaign-specific variation of the old random tables for determining what kind of creature you resurrect as.
Personally, if I were running a campaign, I'd follow some kind of ruling structure like this:
1) If it seems
really inappropriate (for whatever reason) for the character to actually die--they just won't. I might
bill it as the character "dying," but take that particular player aside and try to work out some kind of interesting "rescue" plot or "mind-controlled servant" or whatever they think would be cool. Still probably requires a replacement, temporary or otherwise, but not truly "dead."
2) If the character is under level 5ish and has not yet "died" in this campaign, they get an automatic "freebie with strings." A god, a demonic/devilish figure, a fey being--some powerful entity shows up and offers a deal. If the character already has particular ties (e.g. Warlock, Cleric/Paladin, Druid, etc.) those may factor in--both from whomever/whatever they're sworn to...and possibly the
enemies of whomever they're sworn to. (Always some nice tension there.) Such already-bound characters may even spontaneously wake up without accepting anything, the entity in question hoping that it will be easier to demand service rather than offer a strings-attached deal.
3) If the character is over level 5 or has already "died" at least once, they stay dead, but may be resurrected. Predatory creatures might leave enough of the body behind to track down the rest--or to enable an expensive/difficult resurrection ritual. If the party is cool with it (and the player is interested), this may become a brand-new quest, to restore their fallen comrade.
4) If the party as a whole doesn't want to resurrect the character, but the player doesn't want to let it go, I might try to weave in a more...strange version. For example, if only one other character wants the resurrection, they could make a deal with a hedge witch a la Disney's Ursula: pay a price, get "what you want," even if it's not what you expected. Then I'd roll on a random table of races to see what comes of it. Double-plus side: this actually still leaves open the option of the character's body being resurrected normally--which then leaves an open question about who is "real" or not (or both, or neither!) and other juicy goodness.
Also, all of that aside? I like the 4e method (which 5e more or less uses too) where you have to fail a certain number of saves to actually "die." It prolongs the tension of
dying--keeping that feeling of tension in the air--while keeping death in the uncommon-but-not-impossible range where I prefer it to be. For a party that actually prepares to face deadly situations, there should always be a
chance to pull an ally out, incapacitated but alive, IMO.
Incidentally: I respect others feeling that the game has no tension if you can't lose it all, but for me it's exactly the opposite; if every hand could invalidate all the winnings I've made,
that saps the tension for me. It's why I take a dim view of people fiat declaring that you can
only have tension with a constant looming threat of death.