You only need to reduce the 12VDC to 5VDC to power the ATTINY, you can then use something like a MOSTFET to turn the 12VDC going to the LEDs on and off. You can using the ATTINY's builtin hardware timer to make the PWM smooth and steady.
Here is a simple example circuit....
simulate this circuit – Schematic created using CircuitLab
You can also add a decoupling cap across the ATTINY power pins, but it can work without it at slow clock speeds. Some will say that you need pull down and buffer resistors for the MOSFET gate pin, but you don't. Without the pull dow, the LEDs might blink on briefly when the system powers up before the code in the ATTINY has a chance to initialize the port, and at slow PWM speeds with a 5V driven gate the buffer resistor is unnecessary.