The Oasis Island will be the 4th area on the Fantasy Islands. As soon as you enter you are asked to clean the billboard in front of you by shooting water at it. Afterwards enter the online shop and buy paintballs from the 'Fun' section and launch them at the billboard to change the design. It doesn't matter which design you pick.
The other billboard will be in the second half of this island, accessible after clearing the first half. You will see it as you cross the bridge. Simply clean and paint as before and the achievement will pop.