So I've been looking around but have not been able to find the max stats for each different species of sylesti and more specifically how to get a pet lie that. anyone have an explanation?

Max stat pets are pets that were carefully bred and prismatically philtered over several generations, taking months, and sometimes more than a year, to breed. The max stats that any pet can have at level 0 are 100 in strength, intelligence, dexterity, and Agility, 2,000 in health, and 120 in mana. All stats except for mana can be increased using stat philters (either specifically for the stat in the case of the first four, or using a prismatic philter to increase each of the first four stats by 10 and health by 200). Because each max stat pet takes so much time, effort, and money to create, the breeder has to really love that type of pet and want to make a maxed stat of it. This is why not all species have any maxed stats even available. Anyway, not sure which part of that you were looking for not being able to find maxed stats for each different species, lol.

As to how to get one: either breed and stat philter through multiple generations to create one yourself, or buy one from those that have already done this. Because of how long (and expensive) the process is, they are usually rather expensive, and fairly usually infertile.

thank you! you answered pretty much all the questions :D I'll probably have to get to work on a max sat vulnyx project now :/ XD but thanks for answering my questions!

Max Stat pets result solely from peoples' breeding projects.
There are many species that don't even have any max stats (I'm pretty sure that there aren't any max nytekries or vulnyx, for instance), because of the time (months of work), effort, expense (Philters) and stable space required. It's a labor of love and dedication (and frustration, I expect)

Usually max stat pets are fairly expensive due to the factors involved (100k + gold)

If you're looking for them, you'll want to look in the Breeding Discussion, Pet Auctions, and this Max Stat Project Directory