Based on your
df result, your boot filesystem has less the 60 MB free. Most likely that the updates you are trying to install need more space than that.
A boot volume of 170 MB is quite small. The obvious thing to do is to increase its size, but this requires some time and expertise, so consider some faster actions first...
Try the following
sudo apt-get autoclean and then
sudo apt-get autoremove. This will remove package stuff that isn't used at all and may free some space in the /boot filesystem.
If you know you have packages you can live without, it may be a good idea to remove them.
sudo apt-get purge <package-name> will do that. Knowing which packages you can live without may be tricky, though.
Try the updates again. If you are lucky you may have enough free space at this point.
If this does not work, you will have to resize the boot partition. This involves editing the partition table with a tool like
gparted, and you will have to create a bootable USB drive and boot from it. You should probably allocate at least 1G to /boot to be on the safe side.
I will not attempt to describe how to edit the partition table - it is a delicate procedure that I performed only one or twice... but there are some other posts here that discuss it, like this one.
Edit: Actually there is another question and answer with much higher votes. You may want to read this one.