How are Monster Variant appearances tied to the in-game progression?

According to this reddit thread* the enemy levelling has nothing to do with any kind of character progression through the game. This is entirely due to the number of enemy encounters; i.e. the number of monsters you kill.

The enemy progression works on a "counter" system, and whenever you kill enemies, they contribute a certain amount of points to this counter. (There are a few rules, such as once a certain tier has been reached, certain enemies no longer count, etc.). This is the "Tier list":

0: Starting level
1: Bokoblins --> Blue Bokoblins
2: Moblins --> Blue Moblins
3: Blue Bokoblins --> Black Bokoblins
4: Lizalfos --> Blue Lizalfos
5: Black Bokoblins --> Silver Bokoblins; Blue Lizalfos --> Black Lizalfos
6: Blue Moblins --> Black Moblins
7: Lynels ---> Blue-maned Lynels
8: Black Lizalfos --> Silver Lizalfos
9: Blue-maned Lynels --> White-maned Lynels
10: Black Moblins --> Silver Moblins
11: White-maned Lynels --> Silver Lynels

So, putting it simply, once you reach enough points to reach a new "tier", the higher level monsters will appear to replace the lower levelled monsters (again, this does follow a system, monsters are replaced in a certain manner, so as to not just level up all monsters at once).

In the case of Lynels, however, once the tier to replace the Lynel with Blue-Maned Lynels is broached (I.e. Tier 7) all Lynels (again, apart from the one on Ploymus Mountain) will become Blue-Maned Lynels.

So at my point in the game, the only way I will be able to complete the Compendium, is by purchasing the entries from Symin.

^{*Thanks to l I for providing the link}