It works like this:

Each tourney is worth a certain number of points towards unlocking the locale it is located in, based on its rank (except the official tournaments). If you beat that tourney, you will get a certain number of points toward unlocking that area. KOs, forfeits, it doesn't matter, so long as you win the tournament.

E rank = 1 point
D rank = 2 points
C rank = 4 points
B rank = 8 points
A rank = 16 points

Kalaragi requires 6 points to open.
Takrama requires 6 points to open.
Brillia requires 12 points to open.
Goat requires 18 points to open.

As Lisa said, some people have unlocked areas after regenerating monsters off of CDs. I didn't really test this thoroughly, but I can tell you that entries gotten by encyclopedia, or regenerating different monsters (and then not naming/keeping them) does not help in unlocking. It may be that it only matters if you generate them off of a "saucer stone" (CD, DVD, etc). I don't know.

What about S and Free level tourneys, you ask? I don't know. I didn't test. If the pattern shown follows through to S class, S class tourneys will probably be worth 32 points and unlock any area. I would guess that Free tourneys count as either B or A class, but again, for all I know, they're worth 0 points. Someone else can test if they care to.

Also, I didn't test for the affect of "slumming," so my official recommendation is that you don't do it until you've opened all the areas. Again, someone else can test it if they care to.

These numbers work. If you're having trouble unlocking an area, use these numbers, and the areas will unlock.