You could probably make use of the 328P's analog comparator. Put a stable reference voltage on pin A1 and your pulse on A0. When A0 exceeds A1 the ACO bit in the ACSR register is set. You could poll for an SCO state change or configure the hardware to generate an interrupt and use a simple ISR to do your counting.
You say you need to show pulses per minute; do you need a realtime clock to give minutes count or is the internal timing of the CPU sufficient?
How often do you want to write to the SD card? Once a minute? Once per event?