A big part of Monster Hunter Stories 2: Wings of Ruin is adding Monsties to your party. There are dozen of them in the game, and if you can get an egg, you can add them to your party and fight alongside them.

To get an egg you need to find a den, and because dens are randomly generated in the world, it is impossible to know what is at the end of them. The only way to find a specific den is to find the monster out in the world, make it retreat, then follow it to the den. A retreating monster causes its den to appear, allowing you to get in, finish the fight, and grab an egg.

Retreat is not guaranteed at any point, but you can increase the chances of a monster retreating by doing certain things.