After you defeat four bosses, Colonel will summon you to the Memorial Hall.
Play as X
Before defeating the 4th boss of your choosing, it is recommended to prepare beforehand, such as getting hearts and upgrades. Completing Frost Walrus is highly recommended because Frost Tower is his weakness. Getting the Leg Upgrade from Web Spider's stage is also recommended.
X starts in a pitch black corridor. Move forward and a spotlight will point at X, and another reveals Colonel. Then the background lights up and the fight will start.
Keep in mind that there are no walls to cling, so you have to fight this boss head-on. Colonel will only use his warp assault and sword waves during this fight. His warp assault can be difficult to time and avoid, so using Frost Tower in the air will stall you up for a bit. His sword waves shoots both high and low; the high wave can be dodged by a dash or a well-timed jump. The leg upgrade can help avoid all of the attacks.
Play as Zero
Sit back, relax and watch the cutscene.
Although Zero and Colonel started their duel, it is soon interrupted by Iris. Then Colonel will leave.