The Death of Ba'al on the Achilles was a battle conducted between an alternate timeline Cameron Mitchell and Bosun against Ba'al on the ocean freighter Achilles.
Prelude
After the end of the Great Enlightenment and the Ori threat, SG-1 hunted down and captured the last clone of the former System Lord Ba'al, the last Goa'uld to hold any real power in the galaxy. The Tau'ri and the Tok'ra falsely believed this clone to be the last Ba'al since he was the only one left with a tracking device that Ba'al had implanted in all of his clones. During his Extraction Ceremony, the Ba'al clone warned SG-1 and General Jack O'Neill that the real Ba'al was still out there and was implementing a failsafe device he had created in case all of the clones were killed.
At the same time that the Extraction Ceremony occurred, the real Ba'al used his time machine to travel back in time to 1939 Earth where he arrived on the Achilles, an ocean freighter carrying the Alpha Gate to the United States after the outbreak of World War II. Ba'al and his Jaffa slaughtered the crew of the Achilles and set a bomb to sink the ship and the Stargate into the ocean before leaving. However, Captain Mitchell survived his wounds long enough to toss the bomb overboard and the ship ended up stranded in the Arctic instead.
As a result of Ba'al's actions, an alternate timeline was created where the Stargate Program never occurred. Colonel Cameron Mitchell, Colonel Samantha Carter and Doctor Daniel Jackson managed to escape through the Stargate on the Tok'ra homeworld as the timeline shifted, shielding them from the changes. They arrived in the alternate timeline on the Achilles and ended up spending a year there. A year after they arrived, Ba'al arrived at the alternate Earth, having used his knowledge of the future to seize control of the Goa'uld Empire with Qetesh as his queen and Teal'c as his First Prime. During the subsequent siege, Qetesh learned of Ba'al's time machine and killed him before having Ba'al's fleet decimate the Earth. The remnants of SG-1 formed an alliance with the alternate Teal'c and two Jaffa loyal to him and traveled to the planet Praxyon where Ba'al's time machine was. Colonel Carter was able to figure out how to use it, but was only able to get them to 1929, ten years too soon. During the battle, Carter, Jackson and the two Jaffa were killed while Teal'c was fatally wounded. Mitchell managed to escape to 1929 to repair the timeline alone while Teal'c sacrificed himself to destroy the time machine and kill Qetesh. (SG1: "Continuum")
Death of Ba'al
By the time he reached 1939, the alternate timeline Colonel Cameron Mitchell was prepared for the day Ba'al would arrive and managed to stow away aboard the Achilles armed with two Thompson submachine guns. The activation of the Stargate by Ba'al draws the attention of Captain Mitchell who sends Bosun to investigate. Arriving in the hold, Bosun mistakes Colonel Mitchell for Captain Mitchell who is his grandfather. Mitchell hands Bosun a gun and orders him to the side of the crate containing the Stargate so he won't be vaporized in the unstable vortex as he was the first time. The Stargate activates and two of Ba'al's Jaffa emerge only to be quickly killed by Mitchell and Bosun. Ba'al emerges next and is shocked to find Mitchell waiting for him. Before Ba'al can react, Mitchell shoots him in the head, killing him. The last Jaffa comes through with a bomb and Bosun quickly kills him. (SG1: "Continuum")
Aftermath
Moments after Ba'al and his Jaffa are killed, Captain Mitchell arrives in the hold and is shocked to find Colonel Mitchell who had a distinct resemblance to him. Mitchell identifies himself as "a friend of the family" and tells his grandfather that what happened is "a long story." The two cover up the incident but apparently remain friends afterwards as the alternate Mitchell ends up in a picture that had displayed just his grandfather before.
Mitchell killing Ba'al before he could make any changes to the past restores the original timeline. After the last Ba'al clone is captured, his extraction goes off without a hitch. SG-1 later wonders what the Ba'al clone meant by a "failsafe device", but decide that they will never know, unaware of the events of the alternate timeline. (SG1: "Continuum")