The Fortune Monster egg can be bought in the Shop. The egg can be bought for 30
and can also be acquired from Lucky Roulette, the Tower of Masters and potential Quest Boss rewards. Some consecutive missions also offer Fortune Monster Eggs as a reward.
The Fortune Monster Egg is unique to the others as its name suggests, can bring a player good luck. Monsters acquired from this egg are always the same regardless of level changes, but it offers anywhere from an Ultimate to Eternal monsters. The chances of acquiring a higher grade is unlikely, but possible. Despite this, it is advised not to buy fortune eggs as the spent jewels could have been used for other, more useful purposes.
There is another Fortune Monster Egg, bought from the M Coin Shop. This Fortune Egg should not be confused with the standard Monster Egg as it costs 500 M Coins and only offers monsters from an Ancient to Infinite Monsters. Like the normal version, it is advised not to buy it but instead save the M Coins for Charge Stamina or Energy due to their usefulness on quests/bosses.
A third Fortune Monster Egg also exists in the Honor Shop. This egg costs 200 
and unlike the other two eggs, have set rates. The chances of obtaining an Outer is 70%, Infinite is 25%, Mystic is 4% and Eternal is 1%. All the monsters from this egg are always Plus Monsters.
For more information on what monsters appear in what egg at each level, visit Egg Levels.