I've started preferring hunting via outbreaks, personally.
This is just what I do but:
-I first beat down some outbreak I'm not interested in, completely. I don't think there's any odds boosting from this, but I've always done this and generally get my actual target within 4 cafeteria meals afterward so I'm not gonna stop now =P
-Then I go to the outbreak I'm interested in and beat it down till it says "The number of <Pokemon> is definitely getting lower."
Then I manually count and beat up 15 more. I do not go to the next stage message as there will be less spawns of the outbreak Pokemon, even if you use Herba and hunt with Encounter power 3.
-Then I go to the Cafeteria in Blueberry Academy and order the "Academy Special" for it's Sparkling Power: All Types Lv. 1 boost.
I save right in front of the person selling it, before taking it so that I can reload if nothing shows. BP are quicker and easier to rack up then stocking up on Herba Mystica.
-Then it's back to the outbreak and after letting them load in, if no shiny is there I just quickly put up a picnic and then exit again as fast as possible. Then it's just rinse and repeat till something shows. If nothing shows within 4 attempts and it's a target I really want I'll then bust out the Herba Mystica by going to the outbreak and making a shiny sandwich there, saving before I actually make it so I can reload.
A couple general pointers:
-Save after you find the Pokemon, but make you sure you get somewhat near to it (but not too close), so it can't run away while you're saving. If you fail to catch it for whatever reason, just quit the game and reload. Make sure auto save is turned of for this.
If you load back in and the Pokemon is not there, do not panic. This has happened to me multiple times... just keep reloading till it's on your screen again, which might take a while. I had a shiny that disappeared for like... 8 straight reloads iirc? Not sure what causes this... might be the order in which they spawn, with it being the last one or something... idk.
-There's a lot of Pokemon with moves that can make them kill themselves. For example, Poltchageist at high levels likes to use Memento. To block it from doing so, have a Pokemon that knows Substitute ready. For mons that like to explode, there's Pokemon with Damp such as Quagsire.
-Be careful with False Swiping your target if your opponent knows any recoil moves, or if you're battling in a sandstorm. My own personal false swiper is Ceruledge as it's quite fast when auto battling, and it's Ghost type makes it immune to stuff like Take Down.
You might want to look up if your target knows any recoil moves once you have it in your sights.
-There's a lot of Pokemon with really similar shinies. It can help to look up what the shiny looks like. For example, Litwick has a change it's flame color and it's eye. But the flame color might not be noticeable if the shiny happens to be by itself. Especially with how tricky the lighting can be. Some of the really similar shinies can look just like their shiny simply due to being in a shadow. In Litwick's case I approached it and looked at it's eye to confirm if it was shiny or not when in doubt.