For this you will need to learn about clothes shopping. This can be gotten within a few minutes of leaving the tutorial island.
Once you spawn head straight north to Varrock. When coming from the south enterence past the circle of dark wizards and adventurers guilde. Look for the second building on the left, first build after the only left turn. It is also marked with a green shirt on the map.
Enter it and speak with the standing NPC and ask her to show you her wears. Your achievement will pop once the store page loads.
Video Guide
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