Tip for unlocking rare blades
Rare blades can feel a bit random, and a bit grindy, but here's a few tips to make it a little easier to get those rare blades.
First, you'll want to hoard as many rare core crystals as possible. The more, the better. When it doubt, get one, even if it'll cost you a bit from a shop. Higher rarity will almost always give you a better blade, so focus on getting the rarest crystals you can find.
After that, bind it to a character you want the blade for. Just remember, some characters come and go from your party, and if you bind it to one of them, you'll miss out on getting your blade as quickly as possible. I usually bind to Rex, since he's the main character.
Finally, you'll want to load up on booster crystals. Experimenting and trying different combinations will help, since some booster crystals are more effective than others. Don't forget that booster crystals of the same type can stack, so make sure you stack.
Hopefully this is a help, I remember Xenoblade Chronicles X had a ton of things like this I didn't realize or know about until someone told me or I found it out the hard way.