I saw 2 other guide mention that they weren't sure what level beast taming has to be at to capture specific beasts. I have done testing and can confirm the following.

Evolving does not change the beast taming level required to tame a beast. There doesn't seem to be a significant difference in the stats of a beast egg from evolving. I've had a Trash tier and a Holy tier evolve with less than 1% stat difference. Only real difference in stats is the rarity of the beast. Every Realm is 15 Beast Taming Levels.

If there is any other info that you would like to see, please let me know.