you don't need mystical essences (Mystical and Enhanced essences have the same stats and number of TP, it's just the colour accuracy that increases), for them to be fabled (any species can be maxed), or 4 essences (it can technically be done with just 3 starting essences, but 4 is easier)
To the actual breeding for stats, see this guide, though you have the general gist of it, yes.
To start with, for a project, you'll want to know what your finalised appearance is (colours/traits)
Usually one starts a max project by breeding for the Traits first, then the stats once those are done (then one can dye the final max pair to fix up colours)
Breeding max stats typically takes 1-2 years, and 10+ generations (depends on the starting stats- the easiest to max are fabled Majestic themes made during fests and with 4/4 stat boosters applied and 2/2 condition bonus achieved. The hardest is with wild tamed regular species, since they have the lowest stats)
(our own first nyte max stat project took 8 generations, simultaneously going for 3v (because I did not do it the sensible way), and starting with pets with stats in the mid-50s, and done before the mana cap was raised to 200 and before nurture boosting existed)
You typically want to have access to an infinite genetic tester, too (if you do any back-breeding for cementing traits, you want to only prisma the ones with the good stat rolls, for instance), as well as access to an infert kit (if you plan to sell the final products.)
Doing lots of nurturing so you have enough scales to Nurture Boost pets can also help with getting stats and speeding growth.
Magic pies are also very handy for speeding it up, but are expensive, same with Gender Swap philters.
Aaaand lots and lots of prisma philters. So many. It can take like, 4+ per generation- meaning you'd need more than 30, for a project starting with essences |