You are right: sentence 2 is the only one that gives the correct meaning.
Here is a definition of difficult: the intended meaning is needing skill or effort. What needs skill or effort is the thing that's being done (remembering new words), not the agent (the brain). This is simple to use when the thing that's being done is a simple noun like an exam:
The exam is difficult
When we want to talk about a difficult activity, we use one of these forms:
It is difficult to...
It is difficult ....-ing
We can add a for clause to specify the agent (who or what is having difficulty). Alternatively we can make it the subject of the sentence as in sentence 3, using one of these forms:
John finds it difficult to...
John has difficulty in...
The finds it difficult version is not really satisfactory for the brain, because find in this context means to discover or have an opinion: a person can do this, but the brain cannot. The has difficulty in version would work:
The brain has difficulty in remembering new words.
If we make the agent the subject as in sentence (1), the meaning needing skill or effort is not appropriate. It would be OK with a different meaning- not friendly, not easy to deal with, not behaving well, but this is definitely not the intended meaning.