I'm finding it difficult to find a pattern in the usages of these two. When should I use 業績 over 実績 ?
From a native speaker's perspective, 業績 is a bigger word than 実績. It is more difficult to achieve 業績 than to achieve 実績 both quantitatively and qualitatively.
Unlike what the other person stated, 業績 is also used to refer to the achievements of an individual, not only of an organization. It can be in the field of business or academics and it usually takes decades of hard work to achieve what others might refer to as 業績. A Nobel Prize. for instance, is awarded to a person for his 業績, not really for his 実績. 実績 is too light a word to use in that case.
実績 is word that describes someone's past achievements. Again, it is used to speak of both an individual and an organization. 実績 is used mostly to describe what one has achieved SO FAR. It may or may not be much. For example, if you have spent three months trying to sell X cases of beer and you have succeeded. That certainly is your 実績 but it will not be called your 業績. You need to accumulate 実績 to achieve 業績.
Sometimes, it does not take any kind of serious "effort" to achieve 実績. I am giving a couple of examples from my own life. I have a membership card with a nearby drugstore where I accumulate "points" everytime I buy something there. I get a 500-yen discount for every 10,000-yen worth of purchase. The store calls it my ご購入実績. Likewise, my airline uses the term 飛行実績 for my mileage. Point is that they will never, ever use 業績 for those.
Very simply, 業績 is used to refer to the company's results (企業の実績）. 実績 refers just to the actual result (実際の成績). It is not necessarily a company, eg academic accomplishment =学問上の実績.