Is it OK to attach an LED directly to a 5V Attiny?
From the data sheet

DC Current per I/O Pin ............................................... 40.0 mA

DC Current VCC and GND Pins................................ 200.0 mA

Now each led will be over driven at 40mA (as there is no current limiting resistor) - enough to shorten the life of the led but otherwise not too bad. However running 8 leds will draw a total of 320mA from the microcontroller - together with any current it itself requires to run (depends on clock speed). This is enough to greatly exceed the 200mA total allowed, hence your burned out chip.