Each piece of equipment has a name. "Justice Ball." "Desperado Putter," etc. All you need to do is purchase packs from the store then equip the same named equipment. I did this buying pro packs (which will take longer but you get slightly better equipment) and the set was equipment that started with "Justice." They were all blue in color except the driver which was purple colored. So my set looked like this:
Woods: Justice Woods
Irons: Justice Irons
Wedge: Justice Wedge
Putter: Justice Putter
Ball: Justice Ball
The game will notify you when the set is complete, all you need to do is edit your golfer and equip the equipment with all the same name. To track your progress there are little circles beneath each equipment card. If an individual circle is filled with a color then you own this in a certain level:
Fastest way would be to purchase all Green packs as they are $3,000 each. When my character had decent stats I just played the city park tournaments to get first place money because you don't have to score terribly well to win. Achievement pops when last piece of matching equipment is selected. Hope this is helpful!