As the player levels progress, eggs will reward monsters from different tiers.
Most of the times a good strategy is to just accumulate eggs, waiting for a desired level in order to open them at once, thus maximizing the quality of the monsters that can be obtained.
Level 301 is when the player can get the most out of his/her eggs.
Below there is a table with each minimum reward for every possible result from the eggs according to the player level.
Excluded data from the table
For better reading, some of the information about the eggs were omitted, and they are as follows:
Daily Monster Egg: Besides the 70% base chance for whatever is written in the Daily Monster Egg column, they will also hatch with a 25%, 4% and 1% chance of monsters being from the above tiers.
Mysterious Monster Egg: Same as above, but the odds are now 80%, 17% and 3%.