I managed to upgrade my BanaNAS/Debian Wheezy from 3.4.90 to 3.4.103 by following the instructions here https://github.com/LeMaker/scripts (with bp-update pi all as parameters). However, things didn't work at first.
The first problem was that bp-update (the first download) was not executable. I had to chmod 777 bp-update so it would start. After the script run and rebooted, the version was still 3.4.90. And some things didn't work, like my SD card wasn't mounted. Checking the scripts and reproducing manually what they did (besides bp-update, there is another one on the transfered firmware file, called bp-kernel-update), I found out that the script.bin and uImage files are being copied to the wrong location. They are being copied to the /mnt directory (same as /boot directory), but they should be copied to /mnt/bananapi for this to work. After a reboot, everything was working and the version was shown as 3.4.103.
I'm not sure if this problem is due to the specific distribution I'm using, or the bp-kernel-update script is not correct, but I think at least something should be documented...