Core Keeper

This requires season change from the title screen under Settings > Gameplay Settings > Override Season > Cherry Blossom. Note you cannot do this while in the world. This will work on any existing world. Both white and pink cherry blossoms will work with this. These can be found on the ground in many biomes such as Undergrounds, Clay Caves, Forgotten Ruins, Azeos' Wilderness, Sunken Sea and Desert of Beginnings. Once you have a stack of 10 you can craft them by equipping then using them. Plant this tree and repeat 10 times total.

You can find some areas with Pink Cherry Blossom Trees in Azeos' Wilderness. Pick them up and place them somewhere else.

In Settings there is an option to enable seasonal events, the Cherry Blossom event will place Pink Cherry Blossom and White Cherry Blossom randomly all over the map, collecting 10 of these will allow you to craft a tree. Placing ten trees gets you the achievement. This method is significantly faster than trying to find cherry trees out in the wild.