From the Japanese wiki :
青龍 : Ignores type advantages/disadvantages, except for 'No effect'.
朱雀 : HP healing instead deals damage, except for some skills and abilities.
白虎 : Skills will always hit, but cannot be a critical hit, except for some skills.
玄武 : Turn order based on dolls' speed will be reversed. (Priority and abilities like 'Slow Tempo' still works as normal)
Don't really know if it's correct. Don't even know if 青龍 + Assist Akyuu is something different.
EDIT : It was from the manual from the official site, so I think it will surely be correct.
Oh thank you very much!
Terrain (Seiryuu) 青龍 : Ignores type advantages/disadvantages, except for 'No effect'.
Terrain (Suzaku) 朱雀 : HP healing instead deals damage, except for some skills and abilities.
Terrain (Byakko) 白虎 : Skills will always hit, but cannot be a critical hit, except for some skills.
Terrain (Genbu) 玄武 : Turn order based on dolls' speed will be reversed. (Priority and abilities like 'Slow Tempo' still works as normal)
Ok added the English names to them so in case anyone is running with the wiki or something, having this really helps me out!
The Akyuu thing looks interesting, is anyone in the situation to test this out?