Reset linux user password with ssh key based access
Solution 1:
This is technically probably possible by using some clever scheme for privilege escalation, but it's very unlikely that you will be able to come up with such a scheme if you are not a professional penetration tester. There is a very good reason why there is a hierarchy of privileges in almost any OS in existence and it would be absolutely horrendous security to allow for some easy trick to escalate your user privileges. Your only realistic option would be to wait until another way to escalate privileges is published, if your system doesn't auto-update. But that could take months or years, if there even IS such a vulnerability that would apply to this specific situation.
Another solution would only apply if you have physical access to the device and its BIOS and main drive isn't encrypted - boot from any Linux live CD (or thumb drive, of course) and use chroot and passwd to set a new root password for the installation.
But if you only have remote access and no way to boot from another medium? Nope, sorry. Your system is lost. Reset it and get on with your life. Next time, disable simple password login or use a stronger password.