Is there any exact method to hatching eggs quickly?
Depends on exactly what you mean. Do you mean like doing the entire process faster, or just hatching eggs? I'll tell you all the things that speed up the entire process.
If your lead poké has Magma Armor or Flame Body, the number of steps you need to take to hatch a poké will decrease by 45%, in other words it will take 55% of the steps it normally takes.
What kind of species of pokés you use as parents will help determine how fast the game creates eggs. From highest compatibility to lowest (how fast the game will create an egg):
Same species, different ID nos. and SID nos. (from different games): "The two seem to get along very well." The chance of getting an egg is 69.3%
Same species, from the same game
OR Different species, same egg group, from different games: "The two seem to get along." The chance of getting an egg is 49.5%
Different species, same egg group, same game: "The two don't seem to like each other." The chance of getting an egg is 19.8%
Different egg group (regardless of whether or not they are from the same game): "The two prefer to play with other pokémon than each other." In other words, they will not breed.
Bulbapedia said:
When there are two compatible Pokémon in the Daycare, for every 256 steps that the player takes, the game will decide whether or not the old man has found an egg, with chances depending on the exact compatibility of the two Pokémon.
That quote above provides some handy info from Bulbapedia, and the percentages above the quote are in correlation with the quote.
Now, that may not be the exact answer to the question that you were asking, so I'll try to answer what you may have wanted me to answer.
Each individual species of pokémon has a number of cycles it will take to hatch from an egg. Each cycle is 255 steps, and the number of cycles for an individual species can be checked on the Bulbapedia page of said species.
Common sense tells you that obviously you're going to want to use the path from The Café Cabin all the way down to the Hallowed Tower, but I also have a technique that I use. I don't hatch all the eggs as soon as I get them. Rather, I ride my bicycle up and down the aforementioned path until I have received all of my eggs. Then, I store the eggs in my PC and repeat the process until I have about 50 eggs (since you have a lead pokémon, 50 eggs should be 10 "runs". I then proceed to do a mass hatching. If my time-keeping ability is on track, I believe that process is a little faster.
Be aware, other than the quote from Bulbapedia, all of this information was either from my head or from notes I had already taken on my computer, so take this for what it is. However, do not fret, all my information should be correct.
