What is the difference between
A) By then, you will have shown what you meant to do since the beginning.
B) By then, you will show what you meant to do since the beginning.
Is B grammatically correct at all?
Sentence B does not sound correct to my ear. "By then" indicates that we're talking about a time in the future when the action in question will already be in the past. This is why the future perfect is used in sentence A, which is correct.
A possible way of correcting sentence B would be to say:
At that time, you will show what you meant to do since the beginning.
In this modified sentence, at the future time we're discussing, the action will be in the present or the very near future.
You didn't ask about the word choice, but I'm having a little trouble with the verbs "show" and "do". What does it mean, "to show what one means to do"? Is there no better way to say this? Something like the following would be much clearer:
By then, you will have achieved your longstanding goal.