Most accurate instrument used to measure atmospheric pressure is . . . . . . . . barometer.

Atmospheric pressure is measured by Barometer. However, the most accurate instrument used to measure atmospheric pressure is a Fortin-type Barometer.
Fortin Barometer is the most commonly used barometer for calibration duties. It is a highly accurate instrument that provides measurement inaccuracy levels of between ±0.03% of full-scale reading and ±0.001% of full-scale reading depending on the measurement range.