It seems that the only officially known way to instantly kill someone with a curse was "Avada Kedavra".
So, (spoilers):
considering that was definitely NOT what Molly Weasley used to kill Bellatrix Lestrange at the end of Battle for Hogwarts, how did she kill Bellatrix?
I believe that the only way to kill someone so that they cannot be revived or cured is with Avada Kedavra. It also has no counter-curse, so you cannot deflect it.
However, without immediate medical attention, there are plenty of other things that would kill wizards or witches. You could cut their throats (Sectumsempra), throw stuff at them that breaks bones, poison them, etc. A skilled mediwitch or mediwizard could cure them if they got treatment in time, but they're not going to be getting that treatment during the middle of a battle.
There are probably also spells that have counters to nullify them -- but that would require someone to cast that nullifying spell.
From the wikia page,
This battle ended in the death of Bellatrix, who continued laughing derisively at the efforts of her opponent until the moment she realised Molly had defeated her.
Hence, it can be clearly inferred that Bellatrix treated Molly as a weak opponent and her overconfidence led her to death. On the other hand, Molly was highly angered as Bellatrix was torturing Ginny at that moment and the motherly love gave her the courage to face a death eater.
I can see only psychological reasons behind Bellatrix's death as it was difficult to overpower her when she was in a sane state of mind.
An extract from the wiki page:
... fires a curse that hits Bellatrix right over the heart, killing her.
Though the exact curse used is unknown, I believe she used a legal curse(such as the Stunning curse) and the placement directly over the heart is what killed Bella.
If you remember back to OotP, someone (perhaps Madam Pomfrey) remarks that it was a wonder that McGonagall did not die from so many Stunning spells. So, perhaps it is possible for one to die from a well placed Stupefy or some other type of Stunning Spell, and this is what I believe happens here.
Avada Kedavra is a sure way of killing someone, and illegal, but is hardly the only way someone can be killed using a spell.
There are a few examples of this over the series:
When Filch's cat is assumed dead in Book 2, Lockhart names some obscure spell (the *Transmogrifian Torture) as the one to have killed her.
When McGonagall is attacked by Aurors in Book 5, Hermione says that she was hit straight in the chest and she's not young, showing how even a stunner may cause damage.
Avada Kedavra is highly illegal because -
The book doesn't specify what spell was used. I see no reason to rule out Avada Kedavra though. The curse killed Bellatrix almost instantly which implies Avada Kedavra. The book also notes that
Jets of light flew from both wands, the floor around the witches' feet became hot and cracked; both women were fighting to kill. (emphasis added)
Molly was outraged that Bellatrix was attacking her daughter; everybody was under the impression Harry was just murdered (he hadn't made his reappearance yet). Could it have been something other than Avada Kedavra? Of course - but I see no reason to rule it out especially given the circumstances.
The answer does lie in the fact that death by the brute force of other spells must have done the job. In the movie, it seems Molly hit Bellatrix with a Petrificus Totalus (body binder) rendering her absolutely and totally vulnerable and the force of a general explosive spell like bombarda or reducto gave her the works.
In the book, the author did not specify the curse used. However, in the film, if you'll take a close look at Molly Weasley's wand (watch a clip of it on youtube), the light coming from it is green, which means, Avada Kedavra is being cast nonverbally, and the reason for Bellatrix's body to tear into pieces might be reducto, which is being casted nonverbally.
Molly DID use Avada Kedavra
This question was just answered by Pottermore today:
There’s no dearth of magical talent among the Weasley brood, but Molly and Ginny each have impressive and specific magical skills. Molly’s, of course, tie in with her own personal preferences – so she’s not only marvellous at the magical assembly of feasts fit to feed five hundred, she’s also a dab hand at the killing curse if there’s a witch-gone-wrong in need of offing.
Avada Kedavra is the only spell referred to as "the killing curse"
‘Ah,’ said Moody, another slight smile twisting his lop-sided mouth. ‘Yes, the last and worst. Avada Kedavra ... the killing curse.’
Molly used Petrificus Totalus, the body binder spell, hence the fact Bellatrix was frozen, then she used a strong exploding spell, probably Reducto or Diffindo, whch destroyed Bellatrix.
I believe that Molly used some sort of body binding curse, but it could have been a curse of her own creation, or simply a spell she did not even know and cast out of anger, the spell that made her explode was most definitely reducto and not diffindo. But the correct answer has not been stated by the author, so we shall never know for sure.
From what I saw in the movie, it seems that Molly hit Bellatrix with Petrificus Totalus, and then finished her off with Reducto.
At this point, the Ministry was under Voldemort's control and the Cruciatus Curse, the Imperius Curse, and Avada Kedavra were all legal! So it may as well have been a killing curse.
In the movie, Molly probably used some kind of very strong mummification or drying spell, and by that time bellatrix was already probably dead, but she wanted to be 100% sure she was dead so she then cast reducto to smash her to pieces. I don't think she used petrificus totalus as that is a very basic spell students learn at first year. If there was risk of someone turning into stone and then die by, let's say, falling from the stairs and breaking in halves, i don't think it would've been taught at such a young age. I remember Ron having to use some kind of drying spell to stop the rain at the ministery's office.Also, Molly may have learned the mummification curse during their trip to Egypt, or the drying spell from her usual housework as i think it would be pretty useful.
Since when is a movie a reliable source? Apparently Molly used Duro to make Bellatrix solid, then used Reducto to break her into pieces. In the book, Molly struck Bellatrix in the chest using a lethal curse. Kind of a big difference isn't it. I believe Molly's curse was a well placed stupefy (exactly like Bellatrix's spell which killed Sirius, or the aurors' spell which nearly killed McGonagall)
Molly Weasley most like used Stupefy or Petrificus Totalus to make Bellatrix Lestrange freeze, then shot her over the heart with Reducto or Diffindo, I think it was Reducto. She was angry at her for almost hitting Ginny with Avada Kedavra. After she killed her she gave a grin. HAHA Bellatrix, you got yours.
In one of the movies you hear about molly's recent trip to Egypt where she learned a "mummification spell". So that must have been what she used. But if you pay close attention she was already dying. You could see her stomach and arms pressing into her body as if she were becoming a skeleton. If she used the Avada Kedavra curse she would've fallen on the ground and died instantly instead of standing there and you could hear her wheeze.
When Molly Weasley killed her she wouldn't have used the Avada Kedavra spell. When Bellatrix exploded, Mrs. Weasley probably did use an exploding spell like reducto. But nothing is for sure.
Maybe just strong feelings can create spells. Maybe anger or hatred just made this happen to Bellatrix. When Molly used the odd liquid sucking spell on Bellatrix she probably thought that Bellatrix was dead, came to her senses and used Reducto. In the end she probably used a well aimed offensive spell.
Simple: Bellatrix was killed by her own killing curse that she sent toward Molly Weasley. There are lots of examples of curses "rebounding" in the books, often as a result of a counter-spell. Example, Harry kills Voldemort when Voldemort's killing curse rebounds off of the Elder wand & Harry's simultaneous disarming curse.
