How can I earn the approval of my parents when I feel like all I do is let them down?

Pay key attention to what they do seem to approve and emphasize that. Also, just talk to them. Maybe your just looking at it wrong and really your making yourself feel depressed over nothing.

You first need to approve yourself. Afterwards, sit down with your parents and ask them if you are letting them down and explain you are trying your best.

have a conversation about what their expectations are and come up with a way to meet their needs while being reasonable with yourself and your capabilities

It's highly likely your parents are proud but they just don't communicate it clearly. Spend time with one another and your lines of communication will open up.

We all want the approval of those closest to us. But that doesn't mean we need it. During the times of my life when I thought everyone else was looking down on me I often found out that I was the one doing the looking down. Trying to refocus on yourself and doing things that make you proud of yourself can be beneficial.

By being true to yourself you will have your own approval and that is the only one you will need. Life should not be about pleasing other people or living by someone else's standards or rules. Most parents worry to much, but all they want is their children to be safe, healthy, happy. Try to focus on finding out what makes you happy, what you are good at, what you enjoy doing and you will be on the right path. Listen to your heart. That is where your focus should be and not on trying to earn anyone's approval but your own. Good luck and stay safe, healthy and happy.