Alexakis earned a Bachelor of Arts, magna cum laude, from Harvard University in 2000 and a Juris Doctor, magna cum laude, from the Northwestern University Pritzker School of Law in 2006.

From 2006 to 2007, she was a law clerk for Marsha Berzon of the United States Court of Appeals for the Ninth Circuit and from 2007 to 2008, she clerked for Judge Milton Shadur of the United States District Court for the Northern District of Illinois.

From 2008 to 2012, she was an associate and then a partner at Bartlit Beck Herman Palenchar & Scott LLP, also in Chicago.

From 2021 to 2022, Alexakis worked as a partner at Riley Safer Holmes & Cancila LLP in Chicago, where she focused on government enforcement, investigations, and white collar criminal defense.

President Biden nominated Alexakis to the seat being vacated by Judge Rebecca R. Pallmeyer, who subsequently assumed senior status on August 1, 2024.