This achievement is easy, but it is made harder by the fact that this game does not tell you how to use all of your character's powers. So if you do not know how, let me tell you.
Getting the 25 Plant vanquishes with the Scurvy Scattershot is easy - just squeeze the right trigger when you see a plant and after vanquishing 25 of them you are done 50% of the achievement; The Spyglass Shot is only complicated if you do not know how to use it. Squeeze the left trigger and that will activate the Spyglass Shot, then squeeze the right trigger to shoot it. Vanquish 25 Plants this way and you have the other 50% of the achievement.
You can easily get this achievement in the backyard by either Vanquishing the Plants that walk around or by activating the Flag of Power and vanquishing a few waves of plants.
Good luck and happy gamerscore hunting!