How to translate 'hyper-','super-' and 'ultra-' exactly?
In colloquial English, these words all mean pretty much the same thing (though hyper- is used rather infrequently) so using 超 interchangeably shouldn't be much of a concern.

With regard to academic terminology, your best bet is to look up the specific term in question. One easy way to do this is to find the corresponding wikipage in English, and then click 中文 on the sidebar.

For example, in the case of hypergiant vs supergiant, hyper- is translated as 特超, while super- is translated as 超.

Similarly, for sonic we have hyper- as 超高 and super- as 超.

Finally, for high frequency, we have super- becoming 超高, and ultra- becoming 特高.

All of the above translations were found using the aforementioned wikipage method. From just these few examples, though, we quickly conclude that there is no single translation of the three prefixes at hand.

In fact, hypersonic and super high frequency both use the same prefix (超高) as do hypergiant and ultra high frequency (特高).

Thus, unfortunately, a precise translation must be done on a case by case basis.