The possibility of finding a shiny Pokemon with a hidden ability in the Kiloude City Friend Safari or horde battles

You can chain for shiny Pokemon using the PokeRadar. You have to be careful you don't break the chain. Using repels helps because you won't encounter Pokemon while walking in the grass, instead you will only encounter the ones found with the PokeRadar. X/Y now has grass that will shake, but there might not be Pokemon found in that patch. Stay away from the outer edges of a grass patch, most of the time the Pokemon you encounter will be a different one that you started chaining with. Encountering a different Pokemon will also break the chain. Serebii is showing that a shiny encounter could come around 40 successful chains.

Another feature added to the X/Y games is Consecutive Fishing. Unlike the PokeRadar, you do not need to keep encountering the same Pokemon over and over again. But you MUST be successful in reeling in Pokemon without them getting away. I have been very lucky in the consecutive fishing technique, encountering a shiny around 30-40 successful reels. This can be done with any of the fishing rods. One important note when doing this, DO NOT move from the spot you are fishing in. Once you find a spot, keep fishing there. If you want to increase your chances to get a consecutive fish, get a Pokemon with the Suction Cups ability.

Things that will not break the chain:

• Catching Pokemon,
• Making them faint,
• Running away from battle.
• Using the menu (to move Pokemon around, use items, etc)

I have not tested going into the PSS because there is a possibility it could break the chain if you use GTS, Wonder Trade, etc...

"Global Link" is just Nintendo's term that encompasses all their online services (including the Global Link Website), which includes but isn't limited to Wonder Trade, GTS and the Pokémon Dream World. In other words, every time you read "Global Link", they simply mean 'online'.

The Bulbapedia quote says it all:

"Where possible, all Pokémon obtained from the Pokémon Global Link online, either via the Pokémon Dream World or a Global Link promotion, will always have their Hidden Ability."

So unfortunately no, trading with your friend over GTS isn't going to get you the hidden ability.

However, if someone puts up a Pokemon on the GTS already with the Hidden Ability, and you trade them for it, then you will get the Hidden Ability. This is most likely how your friend got his/her Greninja with its Hidden Ability (unless someone was very kind and put it through Wonder Trade).

A brief overview of Abilities:

Abilities in general (not just Hidden ones) are generated when the Pokemon is first encountered. this means either

• In the wild,
• Hatching from an egg (passed on by the mother or the father when breeding with Ditto), or
• When evolving, If the pre-evolved form had it's hidden ability, then the evolved form will as well.

In other words, there is no way to change a Pokemon's ability via trading. (Caveat, unless there's a Pokemon that evolves when trading, and it's evolved form has different Abilities, although I cannot think of any)

So I can catch wild Pokemon with Hidden Abilities?

Only in Horde battles, and even then only rarely. Plus the types of Pokemon that appear in horde battles are few in number, and doesn't include Froakie or any other starter line at all.

So why does everyone have Hidden Abilities online?

Everyone wants Hidden Abilities as they are generally better than the Stock abilities (although this isn't always the case). Either way, there's the stigma attached to them: Because they are 'rarer', they must be 'better'. Everyone is therefore striving to get them, and that's why you see so many of them.

So where can I get Pokemon with Hidden Abilities?

As Unionhawk states, Friend Safari is your best bet. You'll need a friend of the right type (Water for Frogadier), and then Frogadier can appear in Slot 3, possibly with it's hidden ability.

Side note: One way I've found extremely helpful to check a Pokemon's ability in battle is by using the move Worry Seed, which Budew learns. Worry Seed will change the targets Ability (in battle only) to Insomnia, but before it does, it will flash up the Pokemon's Ability.