Final answer:
The Kepler mission's wide range of accomplishments includes the discovery of many exoplanets but did not discover an Earth-sized planet orbiting Alpha Centauri B in October 2012; this was achieved using the HARPS instrument.
Step-by-step explanation:
The Kepler mission has been an iconic venture into the exploration of extraterrestrial worlds. Investigating the data from the Kepler space telescope, we can address the student's question regarding which stated accomplishment is not associated with the mission. Notably, Kepler has contributed to a plethora of discoveries, such as the first circumbinary planet (Kepler 16b), the identification of Earth-sized worlds like Kepler 22b, the first planet found using public data (PH1), and revealing the existence of dense planetary systems exemplified by Kepler 90. However, the hot Earth-sized planet orbiting Alpha Centauri B was not a discovery made by Kepler but by a different observational method using the HARPS instrument on the European Southern Observatory's 3.6-meter telescope in La Silla, Chile.