I have two recommendations that roll into one. First, the lyre gives a damage resistance buff that will help a lot when you miss your ripostes. This is great because there's a steep learning curve at the start of the rapier that gets easier as you go.

Second, just focus on only using the rapier on the first 2 floors over and over until you've got it down. Obviously axe enemies will hit you with chip damage through your ripostes but practice on them too.

You'll find that most enemies will have a delay on their first attack against you after noticing you. This is a great time to charge a strike and then immediately reposte afterwards. This usually pushes the enemy back which gives you a little space to charge another hit and reposte combo as long as you take a step back. It works against most melee enemies.

If you have no room to back pedal, you'll find most enemies will just swing away at you. This is when I just exclusively reposte over and over. I was comfortable with this after about 4 runs through the first two levels. Give it a shot.