It is actually about 1.8 million gil that you have to spend in order to buy all of the items you need in order to upgrade Vanille's weapon into a Nirvana. But if you have the items already or some of them it won't be nearly as much of a cost.

You'll definitely want the Genji Gloves before you take on the Adamantoise without using a Summon. It also doesn't really help that the video has a person with a party of three completed ultimate weapons already. Which gives you an extra action slot not to mention being stronger. So while it is certainly valid that they killed it without a summon or death. For someone without an ultimate weapon and certain other item it will still prove quite challenging.

But yes, Highwind is the way to go, but only if you have Genji Gloves. If you don't have the Genji Gloves you'll just want to stick with the Summon or Death method until you do.

Also keep in mind that there are three types of Adamantoise out there before you get the upgrade on the Adamantoise. There are the small guys that only have one target and pretty easy to kill at that point. Then there are two that are pretty much identical in appearance except that one has nearly twice the HP of the other. The only way to really easily tell the difference before fighting them is to check their tusks. The one with a broken tusk will be weaker and having less HP than the one with an unbroken one. They do both drop the same item though, just one is much more difficult to kill since it will be more challenging to kill it in one drop without a lot of strength or magic boosts.