a) is difficult, as the word "ambition" has two meanings:
- A strong desire to do or achieve something.‘her ambition was to become a pilot’
- mass noun Desire and determination to achieve success.‘young men and women with ambition’
Meaning 1 above is often used in speech as if it is synonymous with "goal" - " something you very much want to have/do", as https://www.freecollocation.com/search?word=a... puts it.
When it has that meaning, you can indeed use it with "achieve", as the collocations dictionary shows.
However, when it has that meaning, the word "enormous" would not normally be used as an adjective to describe it. So here, "achieve" (or "meet") doesn't work, because the word "enormous" signals that in this sentence, "ambition" is not synonymous with "goal".
That's quite a lot to expect someone in Year 10 to work out, especially as you don't even seem that sure yourself so presumably haven't taught it to them?
I can't think of any word other than "match" that would fit in a), and would take a moment to work out what was going on in the sentence myself.
In b), "motivating factor" is the usual phrasing, but "the motivating factor" would be more common than "someone's motivating factor". Apart from "points", the others are not absolutely impossible-sounding, A person's "something points" (strong points, weak points) are usually their characteristics.