Active: The principal investigator (subject) might have been continuously analyzing (verb) the erratic fluctuations in the molecular structure caused by high-frequency radiation (object) during the controlled simulations.

In the passive the object becomes the subject and the doer goes into a 'by' phrase. A strict passive of the modal perfect continuous ('might have been being analyzed') is very awkward, so the accepted rendering keeps 'might have been' and expresses the ongoing action as 'continuously under analysis'.

The passive must also keep all the details of the original: 'erratic', 'caused by high-frequency radiation', 'principal investigator' and 'controlled simulations'.

The version beginning 'The fluctuations in molecular structure' drops 'erratic', 'caused by high-frequency radiation' and 'controlled'. The version with 'were continuously analyzed' loses the modal 'might have been' and states the action as a fact. The version with 'Continuous analysis ... might have been performed' changes the subject to the action itself and drops details.

Only the official choice keeps the modal 'might have been', the doer, the continuous sense and every detail of the object.

Hence, the answer is The erratic fluctuations caused by high-frequency radiation might have been continuously under analysis by the principal investigator during the controlled simulations.