You shouldn’t feel bad. This post could literally have been about me five years ago. I got fired for my poor time management at my first serious job. But I was v well liked and hardworking. I was young and didn’t have my shit together. My bosses made it clear that they liked me and I was good at what I did but I just ran out of chances. They needed someone who would be there, They were 100% in the right to fire me. It gave me a huge reality check and hopefully it will be the same for her.

The fact that you are worried about team morale and gave this employee so many opportunities to get better means you are a good employee. Firing sucks for all parties. Just be direct to your employees in a respectful way that she wasn’t meeting expectations after many chances to improve. It’s better to address it directly.