It should a be very simple Upgrade from Orion 8.5.1 to Orion 9,
it is just in in-place install over the existing Orion.
Login to your Customer Portal,
Download Orion 9, also double Check that you have an Orion 9 License available.
Make sure you have local admin rights on the box.
Run the Orion 9 Install, Configuration Wizard will run,
Keep all defaults it asks you bar the first screen,
I suggest here you use your SQL Server "SA" Username and Password,
"SolarwindsNPM" account is fine to use on second screen though.
I recommend backing up the following before upgrading:
Backup current SQL Database before upgrading.
Backup C:\Program Files\Solarwinds\Maps
Backup C:\Program Files\Solarwinds\Reports Folders.
If you have any issues, please log a Support Ticket.
Hope it all goes well and you enjoy all the new features Orion 9 has to Offer.