I used to be able to do an update with 2G RAM + 2G swap but that was, I think, before ember, which is very demanding. If you have the disk space to goup to 4G swap, that might do it. Or, temporarily and carefully migrate to an instance with more RAM, do the update, and migrate back.
Whatever you do, take a backup and download it first.
Note that most providers will allow to you migrate to the same disk or a bigger disk. You can’t migrate to a smaller disk. So you need to find an offering which has more RAM but the same disk space.
Eventually I changed provider to get a bigger machine at lower cost. (4G RAM and 40G disk)