Getting a Master Ball:
What you need to do to get the Master Ball is go to the first floor of the Pokemon lab and see Professor Krane. When you talk to him he'll open a secret passage hidden in the floor which will lead to a room which has a chest in it. Inside the chest you'll find a Master Ball. If you haven't been to Citadark Isle at least once you won't find anything in the chest. The Master Ball is best saved and used when you encounter Lugia.

Getting a Premier Ball:
This ball is simpler to get, just go to a shop and buy 10 or more Pokeballs and the shopkeeper will say 'Thank you! As a bonus have a Premier Ball!'.

At Gateon Port when you are interviewed by Acri you recieve 4 different items depending on your answers to the three questions she asks you. The Amulet Coin is the best choice as the Mental Herb, Quick Claw and White Herb can all be purchased at Mount Battle.

Amulet Coin:
Answer 'Yes' to every question

Mental Herb:
Answer 'Yes' to 1 question

Quick Claw:
Answer 'No' to every question

White Herb:
Answer 'Yes' to 2 questions