Pressure sensor, a microcontroller, and an accurate ADC. The 10-bit ADC on the controller can do only fairly rough resolution. The microcontroller needs to do a bunch of math to make this work.
The pressure sensor needs to be designed to take in static air. That is, air whose pressure isn't being changed by the motion alone. This happens if the air intake faces the front or rear of the direction of travel. Ideally it faces to the side. Perhaps the air inside the rocket would do ok without an external port but it's hard to say.