The first puzzle piece is pretty much out in the open. If you draw leaves and rain on the tree in the cart before sending it out, it will clear away the ink around the puzzle piece that's just below the tracks.
In the area just before the Snakeboss fight (with the Bushlings and snakes), head south towards the river. You'll see a tree surrounded by ink. Leaf and rain on the tree and walk through the cleared ink to find the heart crystal. To the south of that, you'll see some rocks in the river. Pickaxe these and freeze the water to get the second puzzle piece.