Here's what you need.

A few grapples and crossbow

A gun

A lot of ammo for gun of your choosing

And I recommend a dino or pike.

Grapple to a tree, shoot all the baboons that don't have the red glow INCLUDING baby's. After they are dead, start shooting the alpha baboon until it's under 85% heath. You will know it's ready to tame when it just walks around. Put taming food of your choice in lost slot of your hot bar, then follow it around and tame.