How to decrease size of macbook pro (early 2011) boot partition?
I think it's impossible (pre-APFS) to delete the first partition. You can expand a partition 'upwards' into free space, but you can't move down a later partition.

If you think that stuff on the boot volume could be deleted until there's sufficient free space, then that might be enough to get you up and running for the time being.
Easiest would be to boot from an external drive and then explore the internal volume from there. (Or using Target Mode from another Mac.) Alternatively, you could mount the boot volume in Recovery's Terminal and delete files from there, if you're comfortable with that.

But most solutions will require you to copy everything off, wipe the disk and then put it all back. A utility like Carbon Copy Cloner or SuperDuper! can make disk images easily.



IMPORTANT WARNING

Before attempting any adjustment to the disk partition, you need to make a backup of the boot volume on a separate device, in case it goes wrong and you wipe the disk.

There is absolutely no value in having a backup partition on the same device as the source data. If the SSD fails or you wipe it; if the laptop gets stolen or catches fire: you've got nothing. 

Backups need to be on a separate physical device.