where can i find

Level 3-1 Marshlands. With Chris on Veteran drive the boat to the middle island (the one with only chickens around) there will be some white eggs to the right of the hut. Then chase the chickens around and and shortly 1 will lay a brown egg. Then quit the level and repeat but playing as Sheva but the chicken will lay a gold egg. And the only way I know how to get a rotten egg is by killing 1 of the majini's with guns and/or jackets on the later levels in the game but not sure precisely. But you will only get the achievement if all 4 types of eggs are on the same screen i.e either carry them around with you until you find the 4th 1 or leave 3 of them in your other inventry and quit the level once you find your 4th egg. Hope that helps.

It really a random drop between snakes majis and chickens

There are 3 types on one island in the marshlands in 3-1 go to veteran and chace the chickens around(you don't have to be sheva)to get the gold eggs,then if you keep chaceing them,they will drop a brown egg then look to the right of the hut for 2 white eggs only thing is that rotten aggs are hard to get and a rare drop from majine

3-1 marshlands, near the center of the marsh or just about everywhere around the marsh. The center is where the chickens lay eggs. White, Gold, and Brown. I think it's around chapter 5 or higher where you find the golden egg. Just kill one of the machine gun majini or rocket majini and sooner or later you should be able to get the golden egg.