Ko, a corrupt detective whose mother recently died, drives away in the middle of the funeral, having been informed that his squad is being investigated by internal affairs for bribery. He crashes into a homeless man who wanders onto the road, killing him. Fearing manslaughter charges, as he is intoxicated, Ko declines to call the police, and hides the body from a passing patrol car. With the body in his trunk, he returns to the funeral and manages to seal the body into his mother's coffin while escaping detection. A few days later, Ko purposely gets into another crash, which conceals the earlier damage and gives him a reason to visit the repair shop. To the fortune of Ko and his squad, the aforementioned investigation is cancelled by a lieutenant named Park. The next assignment of the squad happens to be the capture of a wanted murderer, Lee, revealed to be the homeless man. While searching his hide-out, the squad finds nothing significant, but they meet another police officer who is investigating a hit-and-run incident based on an anonymous tip. As it happens, the hide-out is right next to the site of the collision, and a traffic camera is nearby. The squad examines the low-quality camera footage, noting that the model of the colliding car is the same as Ko's. Moreover, a triangulation of the homeless man's phone, while inexact, points to an area near Ko's mother's grave. It is revealed that the driver of the patrol car mentioned earlier was Park, who outranks Ko, and that he witnessed Ko's collision, though he doesn't know where the body was taken. Rather than formally report Ko, Park black-mails him and demands possession of the body. Ko excavates the coffin and searches Lee, wishing to understand why Lee's body is so important, and finds Lee's cell phone as well as bullet marks on his body - leading him to believe that Lee was already dead before Ko hit him. The cell phone receives a call from a fellow criminal, whom Ko tracks down and interrogates, and who reveals, finally, that Park stole a large amount of confiscated cocaine. However, after storing his profits in a private vault, Lee stole the key and escaped, and right before the collision, was bleeding from a bullet wound caused by Park. When asked about the key, Ko finds out that anything important was always kept with Lee on his body. Ko returns to the grave-site and locates the key, but is arrested by his subordinate, who tailed him after discovering, by means of another traffic photograph, that Ko's car was damaged immediately after the time of Lee's death. The subordinate is killed, when Park uses a crane to drop a shipping container onto his car. Ko gets ready to report on Park, and to turn in himself as well, but Park threatens to kill Ko's sister and daughter. In response, Ko steals a time-bomb from the police basement and inserts it into Lee's body's rectum, and hands the body to Park, whose van gets blasted off a bridge into a lake. Against the odds, Park survives and fights Ko in his apartment, but shoots and kills himself while trying to dislodge a revolver from a fallen bookshelf. In the end, senior police officials decide to cover up Park's and Ko's crimes to protect their own reputations. Ko chooses to resign, and, using the metal capsule from earlier, accesses Park's private vault, discovering an enormous reserve of cash, more than he could have imagined.
The film debuted to stellar reviews at the 2014 Cannes Film Festival in the Director's Fortnight sidebar, where it was praised by critics as a well-made thriller with unrelenting suspense and flashes of humor. Upon its release in South Korea on May 29, 2014, at first it didn't attract much attention or hype, with a lackluster 80,000 ticket sales on its opening day. But through strong word of mouth from viewers, A Hard Day began an unexpectedly popular run at the box office, placing second place for four weeks behind Hollywood blockbusters and Edge of Tomorrow. It also outperformed other local noir thrillers with bigger stars, such as Man on High Heels and No Tears for the Dead. A Hard Day quickly reached its break-even point, garnering 1.6 million admissions 11 days after its release, and by its sixth week had drawn 3.08 million admissions. At the end of its run, A Hard Day had grossed from 3,450,305 tickets sold.