Here is the finished tiling:
To get started:
We can determine some areas that have to be part of a single hexomino and color them accordingly. In the right pear we can narrow down the left part of the pear to two possible pairings of hexominos.
We can figure out the rest of the right pear. If you try having the piece I have in orange in the upper right have its last square go down, you'll quickly reach a contradiction. Then there is only one combo of pieces that works for the remaining space in the pear. This also lets us determine the two pieces of the middle pear that go along the bottom.
Looking at the left pear:
If you look at the available pieces, you can determine that the leftmost piece must include the square directly below it. Also, we have two chokepoints here (in green and blue).
With those chokepoints:
I made the mistake of assuming the chokepoints must belong to different hexominos. It takes a little while, but you'll eventually reach a contradiction based on that. So they actually belong to the same piece, allowing us to finish the right pear as well.
For the next step I took a guess:
Using some intuition I had from the path I took to the contradiction, I just tried putting these two pieces in the top of the left pear:
From there, I just looked at the pieces I had left and found something that worked.