Yes, now you, too, can download the Monster Hunter Portable 3rd demo.
While the demo, which requires codes to activate, is only supposed to be available to members of the Monster Hunter mobile phone fanclub in Japan, someone on the official PlayStation forums has discovered that signing up for the club — even if you don’t own an Internet-capable phone — is a relatively simple process.
Once you’ve followed the above process and acquired your code (you’ll get an extra code to share with a friend, too), you’ll need to create a Japanese PlayStation Network account on your PSP and download the demo using the “Redeem Code” option. The sign-up process is explained in the above link as well.
If you’ve played Monster Hunter Tri, you should feel right at home with the demo for Portable 3rd, as it includes the Deserted Islands area (also known as the Moga Woods) from Monster Hunter Tri, despite the fact that Portable 3rd takes place nowhere near Moga village.
More details on the Monster Hunter Portable 3rd demo can be found here. Something I’ve noticed personally is that the game looks better than still screenshots make it out to be.