First, you make two grammatical errors:
The past of overcome is overcame. The past participle (used to form the present perfect) is overcome. (In this it is like come and become, but not many other verbs).
Secondly, with a third person singular subject ("hard work") have takes the form has.
So grammatical forms of your sentences are:
Hard work overcame the difficulties, and the business expanded.
Hard work has always overcome the difficulties, and the business expanded.
As to the difference between them: you can find dozens of hundreds of questions on this site asking the difference between the simple past and the present perfect. In most cases, both are possible. The difference is in how the writer chooses to present the pattern of events in time.
If you use the perfect ("has always overcome") you are choosing to present the sequence of occasions as having present relevance. This might be that you are regarding the sequence as continuing into the present; or that the events have the present consequences of making the business what it is today; or perhaps both.
If you use the simple past ("always overcame") you are choosing not to present it in that way. The obvious implication is that you are presenting it as a sequence of events in the past: if the business no longer exists, this would certainly make more sense. But this option is still open to you even if the business still exists, and you are running it: it is your choice whether to treat the sequence of difficulties as a finished chapter in the past, or as part of a continuing narrative.
If you do choose the perfect ("has overcome"), then it would make more sense if you use a perfect for the second verb ("has expanded"), because if you are treating the overcoming of difficulties as extending into the present, presumably the expansion of the business does as well.