Spider Mites
I don't have a great digital microscope so this is the best my cheap Celestron would produce. This was also how I learned that it's a B&W and not a Color one. I've had it for a few years but this was the first time I used it. The product though, is making me think about getting a better one that does color.
Here's a close up of the top surface of your sickest leaf. You'll note that it's just a series of white dots. Look at the under-surface, though, and you'll see some microscopie white fuzz and if you look closer, you'll see that the white fuzz is walking around. Spider mites are walking around, sucking on the undersurface of the leaf resulting in the sick looking top of the leaf you see. Kill enough of the leaf and the leaf dries up.
 
There are tons of insecticides available to kill the spider mites. You can also spray off a lot of them with a pressure spray or use insecticidal soap or insecticidal oil. I used the insecticide we talked about last year: water, dish soap & orange oil. I didn't want to bring the plant into my greenhouse so put the plant in my shower and sprayed it there. I did that twice and will look tomorrow to see if there are any living mites left. If not, it can go into my shower. It'll be 50 degrees on Tuesday so some of my plants might go outside to get sprayed - including your Colocasia.