You will probably want to use an em dash:
How I won – and lost – my first employee.
Alternatively you could use an elipsis:
How I won ... and lost ... my first employee.
Further information on em dash and elipsis can be found here
By the way it's a little awkward to refer to "winning" a person. "Won over" is a term that is commonly used, referring to winning a person's support or affection, but to say you "won" a person is not the connotation you probably want, especially not an employee, as it implies that you might think of the employee as being in a sort of master/slave relationship where you "own" the employee because you "won" the employee.
It would be better to say, for instance:
How I gained – and lost – my first employee.
How I found ... and lost ... my first employee.
How I hired – and lost – my first employee.
In the examples provided in the question:
1) How I won (and lost) my first employee.
The use of parentheses indicates non-essential information, whereas this particular information is essential. So the parentheses is not ideal for the intended meaning. Another problem with parentheses is that sometimes people read them without much of a pause (since it's supposed to be non-essential information that the reader can usually speed through).
2) How I won, and lost my first employee.
There are so many rules about using commas that it's generally a good idea to avoid using them to try and mimic speech when you wouldn't normally put them in written form. This usage violates one of the comma rules as another poster already pointed out.
3) How I won and lost my first employee.
This doesn't indicate the intended pauses.