To get an Elderfrost Gammoth Egg, you first need to update Monster Hunter Stories 2: Wings of Ruin to 1.3.0. Once that has been completed, you need to interact with A Quest Board in any village and click on Multiplayer.
Click online play, navigate to the Expeditions tab, and locate the quest (Explore) Ice Eggs. This is an 8 Star quest and is easier to do online over co-op with a friend or a randomer. You can do it solo and be given an AI friend to help, but the AI companion is useless compared to a real-life person.
Once the quest is selected, press OK, choose your Expedition Ticket. We recommend using an Expedition Ticket SR as this gives a higher chance of acquiring a deviant style egg, or in this case, the Elderfrost Gammoth egg, but there is no guarantee.
Explore the area, and locate Elderfrost Gammoth’s den. If you don’t want to fight anything on your travels, bring along a Nargacuga and use its Stealth monster ability not to get aggroed by any monsters. You’ll get to your destination in peace.
Elderfrost Gammoth is not an easy fight. The foe has a massive health pool and incredibly damaging stomp attacks that can wipe out your entire team in one move. But the monster doesn’t change attack types, so bring with you speed types, who can use fire, and you’ll be in for a slightly less rough time.
When Elderfrost Gammoth has been defeated, you can then loot the nest for eggs. Due to Elderfrost Gammoth being a deviant, the egg alters slightly from its base form. Use the picture below to know exactly what egg you are after—the egg is blue and white instead of blue and red.
Like normal, walk towards the exit of the den with your prize and make sure the egg is stored. Then go and hatch it to see if you were lucky enough to get Elderfrost Gammath as a Monstie. If not, rinse and repeat.