If You Walk Into The Various Shops In Fortune City, You Will Notice There Are Free Clothes Everywhere.
There Are Enough Different Clothes In Just The Royal Flush Area To Pop This Achievement, So You Shouldn't Have A Problem If You Just Start Visiting Stores.
*Side Note*
This Achievement And The "Wear All Clothes in The Mall" Achievement's Progress Is Saved Upon Saving Your Game.
- Dying Does Not Save Progress, You Must Save After Changing Into The Clothes.
- This Means You Can Do Both Over Multiple Playthroughs, The Progress Is Cumulative.
Good Luck!