Basic Egg & Cooked Egg: You can pick up Basic Eggs just by wandering around the map. After that, craft a Crock Pot, throw in 3 Basic Eggs, and you'll instantly get the Cooked Egg.
Basketball Egg: Head to the basketball court, pick up the egg, and shoot it perfectly through the hoop to activate the lightning.
Lightning Egg: Found on the map, just hold it in your hand and test your luck by standing around waiting for a lightning bolt to strike you directly.
Chick Egg: Prepare 1 flute and 6 carrots. Lure 6 baby chicks (you can only lead a maximum of 2 at a time) back to their nest so the egg drops.
Volcano Egg: Hunt down and eliminate exactly 8 Cultists wearing bunny ears. Then head straight to the volcano crater to sacrifice them.
Trader Egg (Pelt Egg): The ultimate RNG test! Keep hunting bears and black wolves until they drop a pink pelt (this can take up to 15 minutes). Bring that pelt to the Trader NPC.
Alien Egg (UFO): Reach day 4 to unlock the UFO. Don't just rush in to fight; lure an Alien with bunny ears from the outside into the machine inside the UFO to scan its face.
Ice Egg: Extremely time-consuming. Upgrade your fire to level 5, take an axe into the bear cave, and break the ice block to get the egg. Bring it back, place it next to the fire, and "incubate" it for... 69 to 70 in-game days until the ice melts.
Frog Egg: Switch to the frog event. Grind for 8 keys by defeating green frogs or fishing. Open the door, and you'll see the egg bouncing around. Rush in, grab it, and run away no need to fight the Boss!