Is it possible to power these LEDs with 9V using the arduino and some kind of modified output?
They will run dimmer at 9V.
You can get a 'Boost Converter' to get your 9V up to 12V
60LEDs X 20mA = 1.2 amps
Nice, thank you! I'm assuming I would I need one of these for each LED?
You need just one.
One converter is able to supply up to 4 amps.
You need to feed your 9v power supply (rated at least 2 amps), into the converter.
The converter is adjusted for 12v out.
All the Anodes of the LEDs are connected to the converter + output.
The Arduino then sends output signals to individual transistors that are connected to a LED cathode.
i.e. for 60 LEDs you need 60 transistors.
A ULN2803 can drive 8 LEDs so you need 8 I.C.s
You need 8 x TPIC6B595 serial to parallel shift registers.
You do know these ‘are not’ in a string, i.e. they are all separated from each other.