At the beginning of the quest you will land on Zorah Magdaros and the objective will be to destroy the 3 magma cores before you destroy the last one Nergigante will appear but you don't need to fight him if you don't want to after a certain amount of time he will just leave.
After the magma cores are destroyed you will be brought to the barricade where you will have to weaken him by firing cannons and ballistas at him. when he is weakened enough you can drop down to the boat on the left side of the barrier and use the lever on the front of the boat in order to shoot the large spear which will cause a cutscene and the achievement should pop after the result screen.
*** Spoiler - click to reveal ***After the quest is complete the game will randomly give you limited time optional quests that will allow you to face Zorah Magdaros again in case you are looking to get his armor.