Writing style in academic English

Your supervisor's first objection is against empty "connecting words", as you call them. Since they are empty, you may as well drop them:

To effectively curtail pollution from all sources requires attention paid to the long-overlooked industrial pollution. [To this end T]his PhD research emphasises the need to...

Your argument, rather than some connecting words, should build the connection:

To effectively curtail pollution from all sources requires attention paid to the long-overlooked industrial pollution. This PhD research emphasises the important role of industrial pollution in most immissions today [or whatever your argument is].

The second objection is not against starting sentences with an infinitive, but against splitting infinitives. I don't know whether split infinitives are really bad style or just a matter of taste. Since some of your readers believe the former, I would err on the side of caution. From Wikipedia:

The opening sequence of the Star Trek television series contains a well-known example, where William Shatner says "to boldly go where no man has gone before"; the adverb boldly is said to split the infinitive to go. [...] The construction is to some extent still the subject of disagreement, but modern English usage guides have dropped the objection to it.

Here are my additional two cents: Avoid the passive voice. Who does the "requiring" in your first sentence? Who must pay attention?

To curtail pollution from all sources, researchers and policy makers must pay more attention to the long-overlooked industrial pollution. This PhD research emphasises the important role of industrial pollution in most immissions today.

"Bad style" is probably being too harsh on yourself. It sounds to me as if your supervisor is trying to finetune the final details of your writing, to get it from an A level to an A+ level. This is not unimportant, but the base level is fine, so don't worry too much.

Without longer writing samples, it's hard to give concrete advice. In the referred sentence above, I don't see why you would need connecting words. There is little wrong with saying:

"Effectively curtailing pollution from all sources requires attention paid to the long-overlooked industrial pollution. This PhD research emphasises the need to ..."

If you feel that you must use connecting words, Maybe replace "To this end" with "Hence".

I haven't yet found a single instance of "All in all" where those words fulfilled an actual function in the sentence (and I would be much obliged if anyone could provide me with such an example). Ask yourself: if I leave out these connecting words, does this impair understanding of the paragraph? Getting this right is more of an art than a science, though: the answer to the question is subjective.

All in all, your writing is fine.

Your writing is fine.

I've read your post, and to this end it makes sense.

I've read your post, and it makes sense.

There are lots of words in English that mean very little. Your advisor suggests dropping them - I think they are right.

It may seem strange in your head, but often following one direct sentence with another is the best policy - these types of connectors don't really connect anything. Write the simpler version and then read it to yourself: it probably conveys the same info and is best in shorter form.