I think it depends on what and how bad these bad mistakes were (not asking you to elaborate) and who they affected etc.
If you hurt other people - truly by mistake - then a sincere apology should be enough, we all make mistakes.
If you hurt other people deliberately then a sincere apology. regardless of how it's received, is really needed along with a very honest explanation (not excuses). Doing this is a humbling experience that brings a kind of relief/freedom and will allow you to start healing and move forward.
If the mistakes only affected you, you could try doing this exercise when you go to bed at night, it needs to be every night for a couple of weeks. Doing it completely changed my friend's life for the better, she struggled a bit at first with her mind wandering but soon got the hang of it.
Close your eyes and think about each mistake one at a time, really feel it and the guilt or shame associated with it.
Visualise each mistake as a package you have just wrapped up with the mistake inside, tape it up well and label it with the name of the mistake in big bold letters. Do this for each mistake, really focus on how they make you feel while taping them up and writing the label. Place them into a "shopping bag" after you wrap them. You need to really focus on the feelings. Once you've packed them all in the bag you take them to the "mistake recycle centre"., have a look around, make it a real place in your head.
One by one take your mistakes out of the bag, look at them, look at the label, feel the feelings as you put them through recycling hole. Sort of like the bottle bank - one hole for clear glass, one for green etc. When you've emptied the bag into the recycling box you will get a printed receipt saying "You are forgiven" watch it coming out of the receipt dispenser. look at the receipt, feel it in your hand, read each word individually and believe it. Imagine how that forgiveness feels, how much lighter you feel, how much happier forgiveness make you, really try and feel it in your stomach, like butterflies/excitement.
It takes time and focus but eventually, when you feel guilty about your mistakes during the day, close your eyes and visualise the receipt intently, how the message makes you feel. After a while you just have to briefly think of the receipt to rid yourself of any guilt/shame.
Sometimes we just need to take out the mind trash!