This video shows a DIY mixture for removing urine from a mattress. There are a lot of things in the video that you shouldn't do. First, don't clean your mattress while it's upright. Cleaning your mattress while it's standing vertically will not get to the stains under the covering. You want to keep your mattress horizontal so that you can clean more effectively.
When removing urine from a mattress make sure to use a vacuum to remove the cleaner. Mattresses are full of several layers of padding and removing the urine that has gotten in those layers is impossible without some sort of suction. I'm a professional carpet and upholstery cleaner in Tampa FL and I use professional equipment to remove urine from a mattress, but that doesn't mean you can't.
I recommend using a shop vacuum or a small spot remover to remove urine from a mattress, but you will need to use some sort of cleaning agent. The DYI cleaning solution in the video is not going to be overly effective because there is not enough solution to do the job. I would recommend mixing a 1:1 solution of hydrogen peroxide and water in a bowl or coffee pot. Pour the solution on the horizontal mattress making sure to soak the urine stains. Wait about 20 minutes before extracting the solution. Using the vacuum extract the solution and allow it to dry out overnight. the urine odor and stain will slowly disappear.
If there is still a stain after cleaning your mattress it's time to call a professional upholstery cleaner who knows how to remove urine.