Instructions
Complete the following HR6 quests: The Fierce Black Horn, Black Rock in the Swamp, Blue Sky Pink Earth, Deny the Silver Rathalos and Find the Golden Phantom. Completing them will make the Gaoren mission available.
Complete the quest titled, "The Approaching Gaoren". Beat the Gaoren and the Akantor mission will become available. Be sure to carve 2 Gaoren pincers from the monster.
Defeat the Akantor and carve two Akantor fangs, one Akantor spike and six Akantor scales from the monster. The body of the Akantor can be carved four times and can yield the fang, spike and scales while the tail can be carved twice and will only yield scales. You may have to defeat the Akantor more than once if you do not get the required the materials after the first battle.
Go to the blacksmith in the Pokke Village. Select "weaponcraft" and in the next window select the option "create weapon." Search through the options until you find the Akantor Bow.
Create the Akantor Bow. As long as you have all the required items and 80,000z in cash, the option will become available to you.