Just to let everyone know that a certain bug has been discovered. It's being named the Elemia Island bug. Info below posted from gamefaqs board. If you have started Phase 4 and dived into the 3rd Reyvatel it might be too late already but if you haven't and installed the free Elemia DLC follow the instructions below before you run into this bug. You can of course install the DLC after successfully acquiring Hyuma.
*Koukin96
"Due to a bug, the Hyuma in question, Nam (#44), is unavailable if you've installed any of the Elemia Island DLC. If you have, TnMK and the Hyuma act as if you've already met them; this keeps Nam from being unlocked.
There is, fortunately, a solution if you haven't gone to the shrine yet. Quit out of the game, then scroll up to the top of the Game column in the XMB. Select 'Game Data Utility', scroll down until you find the ATQ data, press triangle, then select 'Delete'. Confirm when it asks you.
You'll lose nothing but time by doing this; what you're doing is deleting the 5G cache install that you had to wait through before your first play. You'll also be deleting your DLC. No worries there, though -- you can redownload it whenever you wish. Just make sure you don't delete anything in the Saved Data Utility -- that's where your saved/clear games and system data are stored!"
Hopefully a patch will fix this issue.