Okay this is getting tired, I'll just give the answer.

Each stands alone not with the rest, (each line means something different)
Finding the link is what I test. (what it says)
A madman named an unlucky beast, (Hojo named Red XIII "unlucky really gave that away")
And aptly so to say the least. (He calls him RED XIII, Nanaki is red)

The blood of the planet, (Lifestream)
That runs over mountains, (Green chocobo)
It has halitosis, (Malboro)
But it can do enough spells to make up for it. (Magic materia)

The connection? The colour, they're all green.

So whoever wants it take it.