Acho attended St. Mark's School in Dallas, Texas. Starring for the football team, Acho had 12 sacks as a senior and 10 as a junior and was a team co-captain both years. He was also the state private school champion in both the shot put and discus.
As a freshman at the University of Texas, Acho played in 11 games, recording six tackles and a sack. As a sophomore in 2008, he recorded 15 tackles and three sacks. As a junior in 2009, Acho started all 14 games and was named honorable mention All-Big 12 by The Associated Press after recording 55 tackles and eight sacks.
After his senior season in 2010 season, Acho was voted team MVP. He also won the William V. Campbell Trophy, given annually to college football's top scholar-athlete, and was a finalist for the Lott Trophy. During that senior year, the Sporting News named Acho one of the 20 smartest athletes in sports, a list that included two other college players and 17 professionals from the four major American sports.
Acho was selected by the Arizona Cardinals with the 103rd pick overall of the 2011 NFL Draft. In his rookie season as a Cardinal, he made 40 tackles, had 7 sacks, and generated 4 forced fumbles. He followed that up with four sacks and 48 tackles in 2012.