My first authorship is being turned into co-first authorship, what can I do?

First, try to calm down and don't react hastily.

Your situation is very frustrating, but it is not horrible. Let's say that the current author ordering would be the final one. You would be what's known as a co-first author. While it would be slightly more advantageous to be the sole first author, in my experience being co-first practically will not have a significant negative effect on your CV (BTW - are you a grad student or postdoc?). This is important for you to realize - the worst-case scenario that you mention is upsetting, but definitely not a disaster.

Some additional points:

1. You can try explaining your perspective to your professor. If you originally decided that you would be the sole first author, you should definitely remind him/her of that. Do this politely, of course, but show your professor this is a big deal for you. This could cause the professor to reconsider, depending on his/her personality.
2. Instead of being the sole first author, you can consider being co-first but listed first. This doesn't make a big difference, but people might associate you with the paper more easily (Whatshername et al.).
3. Consider that regardless of the number of figures, the other author might deserve being co-first. For example, in many papers an experimentalist produces the data and a computational person analyzes the data and produces most of the figures - and they would often be equal co-first authors (even though each of them could think of themselves doing "most of the work"). So I do not know all the details of who did what, but it does not sound completely implausible that the other person did work which justifies being co-first.
4. Regardless of what happens, I suggest you talk with your professor about how to get a more satisfactory outcome next time (if this is relevant for you). Discuss authorship in advance and what happens when things change.

Good luck!

Disclaimer: My Ph.D. is in Theoretical Comp Sci, so I am speaking from a very different kind of experience.

Some Meta suggestions and notes

• I'd say don't calm down - but still, don't react hastily. Especially since there are about a zillion different ways for you to act.

• The whole name ordering and who-contributed-more haggling and intrigues are quite unbecoming. In some fields, authors are listed in alphabetical order, period. Maybe one guy/girl did almost everything, maybe it was a real team effort, maybe someone was simply the higher-ranking person - it doesn't matter. Or rather, maybe it matters, but it doesn't matter to the promotion of science, so it's not part of the paper. It would be extremely rude for an article to include a sentence such as "person X contributed more than person Y".

• Unfortunately, academia is not living up to its ideals, and your Professor is playing politics too much at your expense. You need to consider whether it's more important to you to try and make a stand and try changing these norms of behavior - at least locally and to some extent - or rather endeavor not to cause a scene, maintain good working relations and move on to doing more actual science. I can't entirely fault the second alternative, and in fact it looks like the vast majority of people choose it, but I suggest the first. Of course, there's a third option...

• Maybe this is all dirty politics. Maybe your Professor is not really your friend. Maybe you're surrounded by frenemies. If you adopt this view, treat everything like a cut-throat market interaction and try to make the most of it personally without getting your heart broken. I don't recommend this approach but it's the basis for at least one suggestion below.

• Whatever you decide to do, try to run it confidentially by other people who know what's going on, or who know your Professor, etc. Of course, these people may then run to your Professor, or A's Professor, and mention your plans to them; this might be undesirable, but might also be desirable - getting a kind-of-a-response from one of them before actually acting in a way you can't go back on.

• From your description it seems that A made a significant contribution to the paper; and that he is not involved in trying to get his name as a first co-author. Keep that in mind; avoid antagonizing him and try to avoid courses of action which make him your antagonist on this matter - either because you want to be fair to him; or because you want to work with him in the future; or because you don't want him to try and get back at you.

• How do you know your Professor told you the exact truth? Maybe there are other reasons for making A co-first-author. Try to obtain more information, maybe from other people, maybe in A's lab.

• Many of the possible courses of actions are dangerous to you, some to your Professor, some to others.

• You're suggesting there's some sort of a quid-pro-quo between the Professors. Try to ascertain what your Professor is getting in exchange, specifically for this decision or in general. That is likely to help you decide how to handle the situation.

So, what might you do?

These are mostly mutually exclusive alternatives, and each of them makes some assumptions regarding the above.

1. Insist. Tell your Professor that you're sorry for possibly putting a strain on his relationship with A's Professor, but you do not accept making A a co-first-author. Talk like he needs your permission to do this.

2. Conspire with your Professor. Suggest to your Professor that he should oblige you, and have you talk to A's Professor to explain your case, or arrange with your Professor for it to appear like you threw a fit, or would have none of it (suggestion 1) - while actually this was not the case.

3. Appeal to A: It is not inconceivable you could get A to support your position, in a group meeting or via email. If he's a person with some integrity, he should, and then the co-first-authorship becomes an untenable position, for both Professors.

4. Peer pressure on A: Tell your common acquaintances and friends about what they're trying to do to you, and how A is going along with it. Have some of them inadvertently or advertently talk to him about it.

5. Collective action. Get your Graduate Researchers Union (I do hope you're unionized!) involved. Then you can play the good cop, while your union rep comes see your Professor and tells him "Look, we cannot allow this to happen. If you promote certain graduate researchers at the expense of others, we may have to resort to denouncing your action publicly, with multiple people bringing it up in departmental or all-university fora." Your Professor will likely rethink his position then.

6. Haggle. Tell your Professor, or your Professor and relevant other people involved, that this they're hurting your feelings and your career, that they're demanding quite the sacrifice, and without being compensated somehow you're not willing to accept it (perhaps without naming the exact sanction you are thinking of). Maybe you could get a Post-Doc promise (in writing of course, otherwise it's useless)? Maybe A's lab can do some work for you which they usually don't have time for? Maybe they could promise reciprocation in a forthcoming paper?

7. Accept your fate. Maybe, like @camelcc's answer suggests, A sort-of deserves it anyway. Maybe where you intend to go after the Ph.D. you can establish your merit without people counting positions in author lists. Maybe the price of antagonizing people / making a scene are too high, and you're about to finish and need some peace and quiet to write up your Ph.D. research thesis.

8. Cry bloody murder. If your Professor insists, and you can't influence any of him, A's Professor or A, publish an open letter to both Professors of them, with copies to the Dean/Provost/Rector/whatever it is you got, and send it also the faculty Ph.D. candidate mailing list, put it up on the bulletin board etc. Be super-polite, super-reverential, as non-accusative as possible, say things like "I believe it is inappropriate to misrepresent" rather than "You are lying in claiming" etc. This is a weaker and more dangerous variant of options 5. and 9.

9. File a disciplinary/ethical complaint. Of course, it may be difficult to make anything stick, plus, it very much depends on the regulations and the norms in your university and in your more immediate surroundings. I'm guessing this is considered a highly unusual course of action and is at least frowned up if not worse... also, note you need to make an official demand of all authors to correct the listing, since if you don't have that rejected you can't really complain about anything.

Unfortunately I have seen this sort of thing actually happen - and have seen 1 paper withdrawn, and resubmitted, and another that was never published because of it.

Your professor is looking to get tenure - you are in a strong position. Get your thesis defended 1st, then worry about this.

Id actually refuse to let the paper be published at all rather than this. If you are looking to stay in academia, the 1st coauthor will be a massive deal, unless you have multiple other papers. We are talking the difference between a sucessful academic and the eternal post doc. If you are looking outside academia, whether or not the paper is published will matter little.

If you have to write to the journal to request withdrawl, it will end your advisors chances of tenure, though get the thesis defended 1st, or he'll likely refuse to let you graduate.

If you can't get your thesis done first, go to the department chair now - do not wait. It's academic misconduct, though in my experience you will only make things worse by discussing with your advisor.