In egg hunt you will be tasked with digging out and then depositing eggs before extracting. Every time an egg is dug out a wave of enemies will spawn shortly after. Every so often a swarm will harass the player. After all eggs have been deposited you will need to extract.
When you first land you will be in the starting room, containing 3 tunnels that lead to location of the eggs. On smaller maps, all 3 tunnels will lead to the same cave, but on higher complexities there may be multiple caves.
All of the eggs will show up on the map (hold “M” or “TAB”), allowing drillers to dig straight to them with ease. As mentioned above, when digging out an egg make sure you are prepared to fight a horde. Sometimes you might want to hold off until getting a resupply, or until a swarm has ended. If you are already prepared, you could open up multiple eggs at the same time, allowing you to take out multiple hordes with AoE.
Often the drop pod will land in the starting cave, so make sure you have a way back to there.