I've been thinking over the capabilities and rules of magic, and I think I've thought of an incredibly simple way to defeat Galbatorix. Considering the fact that most elves have the knowledge to do this, and have centuries of wisdom and experience, the fact that they didn't means they must've been really unintelligent.
My theory is based on these four facts:
You can draw energy from the minds of others.
There are thousands, perhaps tens of thousands, of elves.
You can enchant an item to perform a spell under certain conditions.
You can transport an item instantaneously.
Picture this: The elves, perhaps a few dozen of them, join minds and transmute a pile of plants into a very large diamond. Then, once or twice a week for the next few years, all the elves living in Ellesmera, or perhaps the gem is taken to different cities, transfer as much energy from their body without killing themselves as they can, in order to fill up the gems with RIDICULOUS quantities of energy.
Meanwhile, dozens of the elves greatest spellcasters are devising hundreds, perhaps thousands of low-energy, differently worded spells with which they can enchant the diamond with. When the gem was filled with sufficient amounts of energy, the gem would be enchanted with each of those thousands of spells, under the condition that when, and only when, the gem was instantaneously transported near Galbatorix, every single one of those spells, all with the potential to kill Galbatorix, would trigger at the same time, before Galbatorix had the slightest chance to defend himself.
Now, even if Galbatorix somehow had enough wards to block every single one of those spells, do you really think that, given the fact that the books specifically state that Eldunari take several years to develop their full strength (thus putting a severe limit on the amount of energy that Galbatorix might have), that Galbatorix's wards would contain enough energy to withstand the attack of the equivalent of perhaps a million times as much energy as is contained in a single elf's body (which, may I remind you, is many times more than in a human)?
Now, that last paragraph is based on hidden knowledge and likely wouldn't be known to the common elf, but think about Oromis, the 'wisest of the Dragon Riders', and Brom, who both had gems they've been filling with strength for decades? It would only take one moment of inspiration to realise they could do it with the support of the entire elven nation. If I, a humble human who hasn't even used magic, can think of such an approach, then it is obvious that the inhabitants of Alagaesia are idiots.