a faint heart

1. A tendency to experience stress, fear, anxiety, sickness, or discomfort from unpleasantness, graphic imagery, physical strain, or risk. We must warn you that the following video contains images that may be unsuitable to those with a faint heart. I wouldn't advise reading the comments section of this article if you have a faint heart. Part of the hike is along a narrow path very close to a sheer cliff, so it's certainly not for anyone with a faint heart!

2. To have a very timid disposition; to lack the ambition or will to achieve success despite adversity. You can't have a faint heart if you want to work in this industry, I'll tell you that right now. Everyone was surprised that Janice led the meeting with such confidence, as she normally seems to have a faint heart. You can't live life with a faint heart—you need to go for what you want!

a faint heart

timidity or lack of willpower preventing you from achieving your objective.

Faint heart never won fair lady is a proverb which dates in this wording from the early 17th century; the idea, however, was around at least two centuries earlier.