Do I, a Christian, need to forgive someone who will not admit they did wrong, let alone ask for forgiveness?

Yes, you do.  "I the Lord will forgive whom I will forgive, but unto you it is required to forgive all men."

Yes, you do.  You do it for yourself so you can forget about the offender.

Yes.

The Bible permits Christians no excuse. It provides no loophole.

https://www.biblegateway.com/passage/?search=mat+6...

Be aware, though, that the teaching "forgive and forget" cannot be found in the Bible.

SO: we Christians are required to forgive

but

that does not mean that we must allow ourselves or others to be victimized by the same person in the same way again.

Forgiveness does not come from the guilty person admitting they are wrong.  Forgiveness is a demonstration of God’s love to you being brought forward to love another person in spite of them hurting you.

You forgive because it's best for YOU to forgive. That doesn't mean you carry on just as before, since there's (typically) no need/requirement to continue being associated with the offender.

Yes, you do.

I know that's a hard answer, and even harder to do.  I'm usually able to forgive those who have wronged me, when they 'fess up, and/or it's clear they didn't mean to hurt me.  

BUT when they refuse to admit wrongdoing, or don't care that they hurt me, it is SO much harder to forgive!  Worst of all, is when they intentionally inflicted the hurt.  In those cases, I almost always fight a losing battle to forgive the wrongdoer 😖  Without the help of the Holy Spirit, I usually CAN'T forgive the wrongdoer.  I'm not proud of that, but after all I am a sinner myself. 

 Forgiving those who have wronged me, EVEN IF THEY DON'T CARE WHETHER OR NOT I FORGIVE THEM, is only possible with my Savior's help.  Didn't Jesus Himself ask His Father to forgive the very people who nailed Him to the cross, and mocked Him as He died?  He didn't wait to see if they were sorry.  How then can I do less?

I struggle, almost every day, to forgive someone.  It is ONLY with Jesus's help that I succeed.  All glory, honor and praise to HIM 🌹

Phillipians 4:13  I CAN DO ALL THINGS THROUGH JESUS CHRIST WHO STRENGTHENS ME 🕊

God compensates you more and punishes your enemy more when you forgive and he also forgives you more. 

You must offer unconditional forgiveness as a Christian.

Matthew 6:14-15 KJV — For if ye forgive men their trespasses, your heavenly Father will also forgive you: But if ye forgive not men their trespasses, neither will your Father forgive your trespasses.

As a Christian you should always forgive, but if they feel they did no wrong, you still forgive them, for yourself.  This allows you to move on.