Destroy eggs in nest is a mission in Jak 3. After failing to honor the Arena of Death Damas condemned Jak, as well as Sig, to a suicide mission in the Metal Head cave. A nest of metal-pedes had been harassing his artifact carriers, so he ordered them to go into the heart and destroy any creatures they could find.
The PlayStation 3 and Vita versions of this mission are related to a trophy named "Crunched", completing this mission will reward you with a bronze trophy.
While driving deeper into the cave you will be harassed by pod spider, tiny Metal Heads that attack in large swarms and jump onto your vehicle. The Gila Stomper can plow through them without trouble, but keep the gun running (it auto-aims) anyway. Once you reach the heart of the nest (two large caverns with a low ceiling and many twists and turn and obstacles you will be attacked by many bats, just do not stop and keep shooting and they won't pose any real trouble either.
Marked on the mini-map will be 10 egg-like pods that shoot green acid at you if you come close, they're not very tough however so just drive by them and let the gun do all the work. As long as you keep moving none of the enemies should be able to deal any real damage. After destroying the first five go and find the pillar with several normal metal head eggs at the base, destroy these to make it collapse and form a bridge.
Go into the second cavern and destroy the other five egg-pods. Now the screen will go a muddy green, meaning the cave is being filled with a poisonous gas. There's another pillar you can collapse in the second cavern, so find it and race it back out of there within three minutes.