I'm in the process of catching all the Pokemon in X/Y. I've done it for Gens 1-4, and now working on 5 and 6. My process is usually:
1. Beat the Elite Four. You can try to catch all the Pokemon as you go, but in a lot of games, more Pokemon are obtainable post Elite Four.
2. Grind the Elite Four until you have a Pokemon that can solo the Elite Four and a high level Pokemon that can learn False Swipe. XY made it much easier than past games since False Swipe is now a TM. I'm rocking Charizard (Mega Charizard X) with Dragon Claw, Rock Slide, Earthquake, and Heat Wave right now, and a Pangoro as my false swiper.
3. Catch all the Pokemon that are obtainable in the region. Yeah sure you could just transfer all of the Pokemon from ORAS to XY but that's not as fun as catching everyone you can in XY. Sometimes, you can find really useful maps like this one
https://imgur.com/x3V0mjw that will really help you out in that department. By this point your false swiper should be level 60 or so, and should be able to false swipe everything down to 1 hp. Like KillerTyphlosion said, you want lots of different types of Pokeballs. You should have plenty of money from beating the elite four so many times.
4. Organize your living Pokedex. At this point, its time to start making your living Pokedex. I like naming my boxes "1-30", "31-60", etc. That way its nice and easy to see which Pokemon goes in which box.
5. Write down which families of Pokemon you are missing. So like if you have a Bulbasaur but not Ivysaur or Venusaur, there's no need to write this down, as you'll just evolve your Bulbasaur. Use a site like Serebii or Bulbapedia to figure out how to get the ones you don't have. On the same list, write down how you obtain them. Can you obtain them only in ORAS? Do you need to do an event to get them? Once I have all that written down, I like to reorganize them into method of obtaining them. So all the Friend Safari Pokemon are in a list, ORAS exclusives, Y only, events, etc.
6. It's time to head back to the Elite Four! With the readdition of the Experience All in this game, this step became really easy (yet time consuming). Grab your E4 Soloer and 5 Pokemon that evolve from level up (preferably one that knows fly) and run through the E4. Switch out the ones that evolve until you have everyone evolved. Note: Some Pokemon (looking at you Caterpie/Weedle/generic bug of every generation) evolve at something stupid at level 10. That's a waste to take through the E4, it'll be like level 20 after the first fight. Evolve those in Victory Road to save time and space in your E4 runs. You have so many E4 runs that every little bit that you can save counts.
7. Get a Pokemon from each family you're missing! Most of the ones I'm missing are from friend safari/ORAS exclusive/events, and IIRC most of the friend safari ones are also obtainable in ORAS via Mirage Forst/Mountain/whatever, so in your case, you probably have most of these. I'd get the friend safari/mirage whatever Pokemon in ORAS, friend safari is so annoying. If you insist on doing friend safari though, I recommend going to somewhere that has a lot of people exchanging safaris. I use /r/friendsafari and safaricode, and I'm sure this site has something similar. This is another step that can take forever, so I'd recommend switching off on doing step 6 and this step back and forth so you don't get burned out.
8. Breeding time! At this point your dex should be getting pretty close. Slap a ditto in the day care with whatever you need breeded, grab a Pokemon with Flame Body to help hatch eggs, hop on your bike, and go wild. This can probably be added into the mix while doing 6 and 7.
9. At this point you should be down to event Pokemon and Pokemon that evolve in special ways, via trade/stone/whatever. Serebii if you don't know how to evolve them, if you do know, then go do it!
10. Pray that events happen, or find someone that's willing to part with their event Pokemon.
Phew this post got long. Like I said though, I've done this for 4 of the 6 generations. It's definitely tedious, but so worth it when you finish.