Question

What is the easiest method to get shinys in Alpha Sapphire?

Answer 1

I would say Chain Fishing, even though you have a limited amount of Pokemon to choose from, it shouldn't take too long. Or you can use they dexnav which in my opinion is much more difficult.
Source: Experience

Comments

What is Chain fishing?

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Google is your best friend.

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@deoxyspanda Chain fishing is when you successfully hook a water type pokemon several times in a row.

Answer 2

I would say fish chaining or horde hunting

things needed for fish chaining:
1)a Pokemon with the ability suction cups or sticky hold
2)any of the rods
3)a false swiper (optional)

things needed for horde hunting:
1)a Pokemon with sweet sent
2)a false swiper(optional)

If you have any problems there is plenty of vids on youtube