The second and third examples are more formal than the first, and slightly more suitable for use in a “formal letter”.
All of the examples are acceptable in conversation. In a formal letter, one probably should use more-precise wording. In particular, “need to”, “at least”, and “day” should be clarified or differently expressed.
For example, “need to” might be expressed as any of “The terms of your contract require you to ...”, “I'd like for you to ...”, or “You will benefit more if you ...”. “Day” might refer to a workday or shift, a calendar day, etc.
“Do at least this much” might mean “On average do this much”, or might mean “Never do less than this much, on any day”. For example, one might write “You are required to respond to at least 100 messages per shift, on average” or “You are required to average at least 100 messages responded to per shift” or “During each shift you must respond to at least 100 messages”, depending on intended meaning.