This one is tricky because you dont want to wear your best gear when taming as it will break it quickly. Bring a shield, some healing brews, and several pairs of ascendant items to sacrifice to the creature.

It is passive so you will need to agro it, once aggressive, run away from it while waiting for it to hit you with a continuous spray of stomach acid. You will need to block the acid with your shield so it doesnt kill you (you cannot block the single projectile with the shield. It will still hit you and break any equipped armor you may be wearing).

Pay attention to the debuff you get when hit with the spray. You will need 3 stacks of the debuff applied to you after it stops spraying. After it stops spraying, It should then start to inhale you. Once in the creatures stomach you will continue to take damage, you need to quickly open your inventory and throw out 2 pieces of the ascendent quality gear.

You should then be spat out and the gargantar should be asleep. This is your chance to hop on it and get some taming effectiveness. Once mounted a wheel and timer will appear on your screen. Whatever resource the wheel stops on, you will have to consume with the gargantar within the time limit.

(Stone, metal, keratin, wood, meat or Prime meat).

Stone, metal, or wood, just run around holding down the primary action button (RT on xbox) and the gargantar should inhale the resources. For meat keratin or prime meat, you will have to kill some wild dinos to get those resources. So you will need to approach wild Dinos and hold down the secondary action (LT on Xbox) to spew acid on them to do damage.

You will have to do this 3 times in order to get some taming effectiveness. After collecting the third requested resource, you will be dismounted and the gargantar should agro onto you again. Repeat this process until tamed.