Square Enix is releasing a second downloadable demo for Lord of Apocalypse and its close to a full game trial. You can play Lord of Apocalypse, a PSP and PlayStation Vita sequel to Lord of Arcana, all the way until Chapter 3.
The "Lordís Invitation" demo also supports multiplayer, so you can link up and fight Cthulu with your friends. If you decide to purchase the game afterwards you can import save data from the demo into the full game.
Lord of Apocalypse was a PlayStation Vita launch title in Japan and came out last December. Square Enix have not announced an international release yet.