Here are some ways to speed the game up:
1) If you have already played the game don't waste time reading all the dialogue, skip through it all by constantly pressing the A or B button.
2) Don't waste time collecting items, if you want you can go back and collect them after you've finished the game.
3) Run away from any wild Pokémon or use repels to decrease encountering wild Pokémon.
4) Don't do anything that is not needed to complete the game e.g. planting berries, breeding, purchasing outfits and accessories throughout the boutiques, Pokémon-Amie etc. If you want to do these things you can do them after you've completed the game.
5) Transfer high level Pokémon to your game- this goes without saying transferring high level Pokémon to your game makes the game far more easier. Although not as fun it makes it easier to defeat your opponents and speeds up the game in the process. Just make sure your Pokémon doesn't exceed the obedience level because if they do your Pokémon will stop listening to you. Click here to find out more about obedience.
6) Don't worry about EV's, IV's, Natures etc. Honestly these things aren't important in game, you can defeat the Elite 4 and Champion with pretty much any Pokémon so forget these things for the time being. EV's, IV's and Natures are only really important when battling competitively and maybe in the Battle Maison. Besides as you progress through the game the likelihood is that you'll defeat many Pokémon and gain EV's in Stats you didn't want any in.
Remember these things are just some ways to help speed the game up, I'm not saying you have to play the game like this I'm merely suggesting that by following these things you can complete the game sooner rather than later.