The sentence is:
I want to build machines that benefit others in the same way my mother’s life has been bettered.
The sentence is:
I want to build machines that benefit others in the same way my mother’s life has been bettered.
A fix might be "I want to build machines that benefit others in the same way my mother’s life has benefitted from machines." As written it seems unclear/ambiguous rather than illogical. If my suggested revision fits with the intended meaning, it might be even clearer to also list some way the mother's life benefited from machines. (But it's not completely clear if that was the comparison the writer was even trying to make.)
The biggest problem is that the comparison is between an active clause and a passive one. You can correct that by changing the passive clause to an active clause, but you will have to supply a subject (the agent that helped your mother) -- was it also machines?
You probably don't intend any difference between 'benefit' and 'better', so you might as well use the same verb in both clauses.