The sentence you wrote is mostly correct and easy to understand! Here is the original sentence:
"The penguin dad keeps the egg warm by gently holding it on his feet covered with his soft feathers. At the same time, the mother swims far into the ocean to catch fish for her family."
To make it even clearer and grammatically smooth, you could say:
"The penguin dad keeps the egg warm by gently holding it on his feet, which are covered with soft feathers. At the same time, the mother swims far into the ocean to catch fish for her family."
This small change adds a comma and a little phrase, "which are covered with soft feathers," to explain that his feet have soft feathers.
Overall, your sentence is great and easy to understand! Keep up the good work!