Use life energy to restore dead trees and sometimes acorns will fall from them. I often find that doors where you need acorns to progress, there will always be trees nearby that drop a lot of golden acorns. As you go through the game you should be picking up all of the acorns you can.
A quick way to collect them is to check the crosshair in the center of the screen. When you look at a dead tree it turns green and when it's pointed at a living tree it goes blue. This is a quick way to identify dead trees so you can gather acorns. Optional acorn doors don't always have dead trees nearby so you need to save them up as you go through the game. Lockboxes are not a great way to collect them as they don't often have many inside.