This is an unmissable achievement as it's part of the story.
After handing in the cat to the little girl she'll ask you to talk to her dad who will ask you to get some lumber, he'll give you an axe for this. After helping him he'll ask you to talk to his dad who is at a pile of rubble, a former clock tower, that you'll have seen earlier in the start, he'll ask you to find some materials in the Great Forest to help in rebuilding the clock tower. Progress farther into the forest and you'll come across your first boss fight after meeting someone before hand, to defeat this boss it's pretty easy.
The boss will attack with branches that will show as red indicators before they come out of the ground, stay ahead of the red indicators and after the second time the weak point of the boss will appear, a large wood worm, which will fire an electrical ball that can do lingering damage on you, get in as many hits as you can and try to avoid being hurt too much by the worm's attack. Rinse and repeat until the boss is dead and the achievement should pop.