Both of your statements convey a similar meaning, but the first one "Doing something that potentially will fail" is more commonly used and considered more grammatically correct. However, you can also rephrase your second statement to make it sound more natural, such as "Doing something that has the potential to fail." This phrasing still conveys the same meaning as your original statements, but it sounds more natural and is often used in everyday conversation.

I respectfully disagree with Richard. I think we can write that something indeed "potentially will fail". It's an uncertain statement about the future. The rules of our language are complex and, frankly, they change depending on who you ask, so I tend to just judge by my ear. I suggest that both "potentially could fail" and "potentially will fail" are possible and that they have basically the same meaning, and a native speaker might say either one. They don't connote exactly the same thing. Using "could" is more hesitant. It suggests the speaker doesn't want to make any strong statements either way. "Potentially will fail" is a more confident statement about the likelihood of failure. It's not necessarily a statement of higher probability of failure. The difference is not about the probability of failure; it's the confidence of the speaker in his own statement.

“potentially will fail” = “might fail”

Ahmadi is correct, I would like to add that the second phrase could easily be reworded to "...doing something that might fail."