Accumulate the indicated number of Hunters Points in African Safari mode to unlock the corresponding weapon.

.44 custom handgun: 5,000 points
12 gauge custom shotgun: 12,000 points
.410 over under custom shotgun: 15,000 points
.300 custom rifle: 19,000 points
.505 custom rifle: 25,000 points
.243 custom rifle: 32,000 points
.416 custom rifle: 40,000 points