What do I say to people that ask about my scars without making them uncomfortable?

The ideal is for you to feel comfortable in yourself to either be open and honest that you've overcome some hurdles and trauma in your life, or tell them it's not something you wish to discuss, but thank you for asking. Either way, you don't have to make yourself feel uncomfortable and pressured to tell someone if you're not sure - especially if you're not sure you can trust them. If you're confident in the way you deal with this question, then they're less likely to feel uncomfortable.

Say, “These are my battle scars, it shows that I went through hell, and made it back alive.”

I know how hard this is by experience, and especially if they are not healed yet. If they are scars always remember to say "i'm stronger now" or "i have learned how to cope now". You can always say, "i was going through a really rough time and i was not sure how to cope, but i'm better now". If that's the case, you are not lying to them and you are saying something that's beneficial to the both of you. Side note, scars show your strength!!

you can say that you where going through a hard time and now you are doing better and that they where a part of you life that you struggled with

You can say that they were a way of coping when you were going through a particularly hard time, and that looking at them is a reminder of how far you’ve come since then

They are always going to feel uncomfortable. Well not necessarily uncomfortable but worried. Just say whatever you are comfortable sharing.

Well, it depends on the situation and how much you trust the person asking you about your scars. If you're in a public place where you can be easily heard by strangers around you, you can simply say that an accident occurred. If you don't quite trust the person with telling them about what really happened or you are in an environment that makes you feel uncomfortable, you can express your discomfort and that you would prefer discussing it another time. If you are in a private area where no one else can hear you, and you really trust the person, you can ask them if they feel comfortable discussing self-harm issues before you proceed.

Tell them the truth. There is no reason to feel embarrassed. Your struggle is something personal and it might seem scary to talk about it. However, if people ask they are either curious or they really care about you and want to know if you're okay. If they ask, tell them that about your struggle, don't go into details if you think they would feel uncomfortable. You can say that everyone goes through some tough things in life and they are individual and intimate. Remember you always have the right not to answer.

Don't give them a questionable answer. Answer truthfully then I bet they'll understand. That what I had to do.

Just say that it is something that's happened in the past, and that you're getting help. This will calm the situation.