I guess by now you are familiar with Zorah Magdaros and Xeno'Jiiva right? Or no? Wait, what? Okay, if you're new then you probably don't want to read this because this might spoil your adventure but if you've progressed enough in the story and about to face them, all the more reason to read into this. If you're a veteran hunter or way past these two, sorry this article might not be for you.
Zorah Magdaros and Xeno'Jiiva are like special monsters in this game as you cannot normally hunt them via usual quests like the other monsters. They are Elder Dragons part of the main story and upon completing their initial quest under Assigned Quests (story mode), they will randomly appear in your Optional quests randomly (you need to do them right away as they disappear after some time).

Zorah Magdaros

Now for this quest, initially you would want to destroy all 3 cores as much as possible. This is not a requirement but more parts destroyed more chance rewards in the end. Start with the one in the middle as the nearest, then the one on the lower part. Watch out for the explosions, you can see the lava building up before it goes off. Just visually confirm it or stay at the side of the core with no cracks, lava will not come out from that spot. Deal with the last one while also destroying parts such as these along the way. You might want to farm the minecrops as well. Eventually Nergigante will come but you don't really need to face him, he'll fly away after a certain time. There is a time limit to these, if you were able to destroy all 3 cores before that just wait it out until you get transported via Wingdrake to the barrier.
Now on to the final phase of the operation. Just load up the cannons (up to five balls) and shoot at Zorah Magdaros. Keep in mind you can adjust the angle by moving the cannons on either of its sides. Aim at the breakable parts until they get destroyed. Just watch out for the small flying monsters, they are there to annoy and distract you. You can also use the ballistas here, one ammo for shooting and one for restricting the Zorah Magdaros' movement for a short time. Also always watch out for meteorites from time to time. You're probably too busy doing something though to be able to notice this so just be ready with your potions and stay at close to full health all the time. When the quest prompts you to use the dragonator, go to the leftmost portion of the barrier and jump down to use the switch and poke Godzilla's ass for some awesome damage. Use the cannons here as well to make the most out of the distance you traveled. Do this until you finally draw the Zorah Magdaros to see. Oh, by the way, apart from the faint count the quest fails if the barrier gets destroyed which happens if you weren't able to do enough damage in due time. You may use the video below for your reference. Enjoy your Zorah Magdaros set, you'll eventually replace it with your armor of choice once you are comfortable enough to take down those monsters.
Xeno'Jiiva
Spoiler alert! This is your last chance to turn back. No? Okay, this is the final boss. This is one huge ass elder dragon that you need to cross out in your long list of victims. Don't get intimidated, he is fairly easy if you know what you are doing. The attacks are slow and the animation is enough to see what's coming. Upon completing the first quest "Land of Converrgence", the optional quest "A Light Upon The River's Gloom" will appear from time to time. Don't miss out on the opportunity as this will disappear after some time. Unlike Zorah Magdaros, you will have to engage this one in actual battle.
This guy is really slow but do not underestimate it as it has a lot of attacks that can one shot you. What you want to do is stay below it or near the front legs. Take not of the weakpoints and breakable parts. I usually start by severing the tail first and try to carve it twice when I find an opening as you might not have enough time to carve everything without the right skills.
