Monster_Hunter_4_JPN_3DS-Kirin MinFW: 5.1.0J
Monster_Hunter_4G_JPN_3DS-Kirin MinFW: 8.1.0J
From my understanding every game that uses max 5.x SDK should work with the CFW just fine, everything never needs a Gateway Card to function however.
I try to test Monster Hunter 4 JP on my 3DSXL 4.3...