That is a backwards setup of the partitions.
Normally the order should be 1st partition sda1, 2nd partition sda2, 3rd sda3, etc.......
Was windows on this computer and it is no longer bootable?
sda1 looks like what Windows would use as C drive.
Do you know why sda3 has bionic for a label?
I guess the Mint installer program did this backwards partition labeling.
Not sure why.
I hesitate telling you to use one of the Puppy boot loader install programs to make a boot loader to boot all OS's with.
I think sda1 not being the first partition would be an issue.
I will give you this much info.
How to do a frugal install of Fossapup64.
Have the Fossapup64 9.5 ISO located where it can be accessed.
boot the computer with the Fossapup64 USB.
Run Frugalpup-flexable frugal installer
On the main window are selection buttons.
Select the Puppy button, to do the install.
Go through install process, selecting to install to sda3 partition.
Note:
When selecting the partition to install to.
A window pops up, giving option to make a directory(folder), to put the frugal install in.
I make this directory and usually name it, the name of the Puppy version.
Carefully read that windows info.
Press enter, makes the directory, not the OK button.
complete the install.
That is the frugal install.
The fossapup64 files inside a directory.
I am going to let someone that knows how to add a Puppy menu entry to the Mint boot loader config files.
Tell you how to do it.
Sorry, I am just not sure with your setup.
ANYONE, that knows for sure, willing to help?
Note:
All the info you have provide, is a great help, to exactly understand, how you are presently setup.