How can I turn off a 3.3V circuit with a 3.3V microcontroller
You should show us what circuit you've tried, but your simplest solution is this case would be a single P-channel MOSFET.  







simulate this circuit &ndash; Schematic created using CircuitLab

When your ATtiny's GPIO pin is high, the MOSFET will be switched off, and when the pin is low the MOSFET will be switched on. Make sure you connect the Drain &amp; Source pins the right way! If you get it wrong the MOSFET's body diode will conduct and you won't be able to turn it off.

Note that this simple circuit will only work when you're switching the same supply voltage that your ATtiny runs from, and requires a MOSFET with a suitably low gate threshold voltage spec.