Though not entirely story related, if you are just that bad at playing you may very well miss this trophy. After every battle, you will see a Results screen charting the time spent and damage dealt to you in stages of a tree's life (sapling, sprout, tree, and cherry tree). The earliest you will encounter a fight will be on your way back to Kamiki Village after having obtained the Power Slash ability (Tachigami) in the Cave of Nagi. Simply defeat the imps you encounter and you shouldn't have any trouble getting this.
If you do, you will have plenty of battles throughout this game, especially if you're going to do everything available, so you will find that this won't be that hard to accomplish. You can always return to earlier locations with stronger weaponry and QUICKLY demolish any of the demons, if you still haven't obtained it later on.