It is a mitzvah to destroy Amalek (Rambam mitzvah #188, Chinuch mitzvah 604).
The Chinuch seems to understand that this is both a mitzvah upon the Jewish people and upon every individual.
זאת המצוה מוטלת על הציבור כולן... ובאמת כי גם על כל יחיד ויחיד מישראל הזכרים... בכל מקום ובכל זמן
This mitzvah is incumbent upon the entire public... and in truth is also upon every male individual of Israel... in every place and at all times.
Without overcomplicating things, the Minchas Chinuch (based on his comments both ad loc and to mitzvah 425) seems to understand that it is a mitzvah to kill an Amalekite even in the face of danger and personal risk, even for an individual. (This is as opposed to some who understand that an individual is not required to perform the mitzvah in the face of danger, and only in the context of war, with the tzibbur, does the mitzvah override the danger.)
According to the Minchas Chinuch, why didn't Mordechai (as an example of someone who seemed to be interested in keeping mitzvos with mesiras nefesh in Shushan) kill, or at least attempt to kill, Haman, a known* and available Amalekite?
- See Targum Sheni to Esther 3:1, and Maseches Megillah 13a