"You are very busy at work, you need to pay attention to your health."
I have seen lack of consistency across many modules in this course. I think there are two possibilities that are not mutually exclusive:
1) The DL Chinese tutors are not well organised and do not collaborate with each other.
2) The DL Chinese tutors are collectively trying to drive us all nuts.
- 身体 can be omitted.
- "在工作很忙" is grammatically incorrect, unfortunately; you could omit the 的 (and arguably the 了 as well, depending on the intended meaning) from the original sentence though. "你需要注意健康", while being a literal translation of the English words, sounds very awkward and a little rude, as if you were ordering the individual to watch out for their health. "要/应该注意(身体)健康" is the more natural and polite expression.
The 了 particle has countless uses in Chinese, one of which is to complement the intensifier 太. When I was studying Chinese at a school in Jilin province, one of my tutors was a young man whose father was a professor at the school. His father had written an academic book of considerable size solely devoted to the uses of 了.
I can understand your confusion. Chinese doesn't use 忙 in exactly the same way as English uses "busy", so having 在 would be confusing in a context such as this one.
And the reason for 健康 here is that 身体健康 is kind of a stock expression when referring to physical health. You could, though, simply say 注意身体 or even 注意健康 to mean "take care of your health" and it would sound perfectly normal.