There are a few slightly less frequently used words in that sentence so let's make sure we have the vocabulary clear in this context before we look at the grammar. "Emancipation" means the process of being set free "Fillip" means a boost or stimulus "Impact" (in this context) means a strong effect With regard to the grammar, as you correctly pointed out, the subject, verb, and object in the first part of the sentence are easy to identify and, if you know the meaning of the vocabulary used, then the first part of the sentence "The emancipation of the human mind offered an immediate fillip to a movement" is fairly easy to understand. The more difficult part of the sentence is the second part that starts with "of which...". You'll probably find it easier to understand the sentence if you know that "of which" is just a (fairly formal) possessive form that can almost always be replaced with the less formal "whose" in this kind of sentence. We can also replace "no less powerful than" with the simpler "as powerful as". If you re-write the sentence using "whose" and "as powerful as", it becomes: "The emancipation of the human mind offered an immediate fillip to a movement whose historical impact on the human condition was as powerful as the Reformation." Or, using simpler synonyms from the vocabulary we covered at the start of this answer: "The freeing of the human mind gave an immediate boost to a movement whose historical effect on the human condition was as powerful as the Reformation." Is that easier to understand? If not, leave a comment and I'll try to answer again.

I am not surprised you cannot take in all of the sentence in one reading. It is exceptionally long. And at the point that gave you trouble does jar a bit and does not easily scan. "The emancipation of the human mind, offered an immediate boost to an historical movement, whose impact was no less powerful than the reformation.