The first question, 'How to improve that?' is a sentence fragment; it's incomplete. Also, it's asking the wrong question. "How to improve that ... I have difficulty in listening" ? How to improve ... the difficulty? You want to know how to make it more difficult to listen? I would think what you want is to improve your listening, not the difficulty. But the word that is ambiguous in this phrase.
When you add the subject "I" and the preposition "on", as in "How can I improve on that?" You slightly improve the ambiguity. "How can I improve on ... I have difficulty in listening."
To be clear, you'd make a full sentence of something like "How can I improve my listening skills?" Or something similar, but if you need to use 'that', the latter two examples are fine.