Whatever he aspired to achieve, they were hindered by his jealous stepbrothers.
Whatever he had any aspirations to, they were hindered by his jealous stepbrothers.
How 'they' is ambiguous in both the sentences... As far I can tell 'they' is referring to 'whatever he aspired' so how can it be ambiguous as there isn't any other noun? Or actually is there here vague reference of a pronoun being said as an ambiguous reference to some other pronoun?
Whatever he aspired to achieve, they were hindered by his jealous stepbrothers.
It is not clear what they refers to. I'm not sure that I would describe it as ambiguous, that would imply that there are two clear alternatives. Here there seems to be no precisely correct referent.
I would usually expect to hinder a person or an activity. He is a person, but singular so I doubt that they could refer to him.
Whatever he aspired to achieve would be a goal. You don't hinder the goal itself, you hinder the process of reaching the goal. He wants to speak French, his learning of French can be hindered, but this again would be singular.
The second sentence has similar issues, nothing quite matches the they
We might say
No matter what he wanted to achieve his efforts were always hindered by his step brothers.
Whatever aspirations he had, they were hindered by x.
To use they, you have to use aspirations, the noun. They refers to the aspirations.
If you keep your sentence:
Whatever he aspired to achieve, they were hindered by his jealous stepbrothers.
Then, you have to say it:
Whatever he aspired to achieve, it was hindered by his jealous stepbrothers.
It refers to the entire first clause: whatever he aspired to achieve.
