He seems to agree with most of us in that they're trying to conquer the world.
This implies that he seems to agree with you, and "in that. . ." clarifies what exactly he agrees with you about.
He seems to agree with most of us with that they're trying to conquer the world.
This is incorrect because "with that" is not a phrase that means something here. It tries to pull the word "that" in two mutually exclusive directions.
He seems to agree with most of us with that.
This is fine. It would be better if it said "on that," but "with" is fine too.
"He seems to agree. . . that they're trying to conquer the world."
This is fine.
"That" serves as a noun in the first, and a connector in the second. When you combine the two, these contradict each other. The one word cannot be both.
In a sentence, "that" must be used either as a pronoun or subordinating conjunction, not both.
The second sentence is awkward because subordinating conjunctions do not generally follow prepositions like "with" to introduce clauses.
Also, "with most of us" is already functioning as the object of the verb "agree." Adding another "with" with is confusing. What is it supposed to be doing? The reader can't tell.