The Attiny Controllers are a complete family from little 8pin Controllers up to Chips with 20pin's.
Nearly every AVR Controller has an SPI Port that's required for the nRFChip. Software SPI is an Option too, but very slower.
The Tiny should have an external Interrupt too, to use the INT Option of the nRF's and few other free Pins to handle the steering lines of the nRF.
I think the limiting factor is the Programm space of the tiny Controllers, but that depends of Your application too.
A simple description of handling the Chips You can find here: https://www.mikrocontroller.net/articles/NRF24L01_Tutorial
Sorry that's in German, but Code and Schematic's are International.