Level shifting between SD Card and Lipo-powered microcontroller
For the 3 output signals, use a 74LVC3G16 triple logic buffer with Vdd connected to the SD Card 3.3V supply. This logic family's inputs can take up to 6.5V and have no Vdd clamp diodes, so the ATtiny can safely drive them even when powered with 4.2V. 

For the input side you might just get away with a direct connection. Input high voltage of the ATtiny is permitted to go +0.5V above Vcc, but you are powering the SD Card through a step-down converter so it cannot output a voltage higher than the battery voltage anyway. 

With a fully charged battery the ATtiny could get as much as 4.2V, while the SD Card's logic high output is nominally 3.3V. This gives a logic high level at the MCU of 3.3/4.2 = 79%, which is above the required minimum of 70%. However the SD Card spec says it might only manage 0.75 * Vdd which is not enough. To ensure that the output reaches 3.3V you could use a 74LVC1G16 single buffer gate.

You might also consider redesigning the circuit work with the MCU's power supply regulated to 3.3V. Regulators such as the MCP1700 have quiescent current of less than 2uA, and will help prevent possible misoperation of the MCU due to rapid supply voltage changes.