Getting proper credit for a paper: author order

Question

I am a PhD student and I submitted a paper formally co-authored with my advisor months ago. The core idea of the paper is mine. During the first (major) revision, among other much needed, yet very time-consuming, improvements I had to implement, I had to take the methodological section over in order to develop a more compact, precise, and overall stronger argumentation. A further revision request, while appreciating my effort, now requires to hugely revise the (relatively small) part he developed and wrote. In spite of my great effort, the author order is established by my advisor as alphabetical and I feel I am not getting enough credit for my work. My advisor does not seem open to other options, such as specifying contribution in the appendix of the paper while keeping the alphabetic order of the authors.

An author listing convention is not defined in my field: alphabetical ordering is not uncommon, although first authorship undoubtedly has a relevance.

Overall, I think I have contributed from 80% to 90% of the paper. I do not know what to do in order to get my effort more properly acknowledged (I strongly desire so), nor I know if anything can be done at all.
I do not even know if this matter is worth the struggle, or maybe it is better (as for our student-advisor relationship) to let it go.

EDIT: thank you for your detailed answers. I appreciated both of them. I accepted @Buffy's answer for the slightly more practical approach - which I needed most - to the problem. I also felt the sympathy in @Titus' answer, and I appreciated it very much.

Answer 1

The good will of your advisor is more important, I think, that fighting for a minor issue over one paper. Hopefully this isn't your last or best paper. If alphabetical is acceptable in your field then let it go.

You could fight it to the death, of course, but it would be you that is more wounded than your professor if you don't get a good letter to boost you to your next career level.

If you do the right thing and reach that next level, then you will have more control over things. But you have to get there first.

Answer 2

I suppose the alphabetical order is in favour of the supervisor. Unfortunately, if the excuse is indeed valid for the field you cannot do much. You can try and challenge it based on the practices of target journals, but you should be prepared for some confrontation.

An informal convention in many fields is that the PhD student gets to be the first author and the supervisors follow. It is within the power of the supervisor to uphold it but it is also violated both in favour of an undeserving student and to the detriment of a deserving one. Field conventions do vary, but as long as first authorship has weight and there is not a very good reason I am thoroughly in favour of first authorship going to the PhD student. I can only express my sympathy.

In my experience, a standard situation for publications stemming from a PhD is that the major bulk of the workload falls on the PhD student and supervisors undertake some rewriting (introduction/ conclusion/ discussion), polishing and getting the paper published. In that context, it is natural for the student to undertake as it is part of the learning process of the PhD.