I'm another one who thinks that the framing you are using doesn't represent what is actually going on OP.
I am probably the sort of person that you would describe as "gender critical". But it's not how I choose to describe myself. I would describe myself as a feminist and a women's libber. I want girls and women to be liberated from the oppression of patriacrchy and I want us to have equal rights and socio-political status in the world.
I've held those views since teenagehood and I'm still on the same path of resistance as the one I started out on. In the 80s and 90s if seemed like things were improving and thanks to the brave and brilliant work of the feminists who had gone before me, things were really changing.
Then the backlash came. It came in various forms and guises; pornography, queer theory, the redefining of prostitution and sex trafficking as "work", neo-liberalism, etc, etc. And transgenderism was another prong of that backlash and therefore something to be resisted as, like the other elements, it was founded on sexist, misognyistic, male supremacist ideology. It was all part of the same thing and based on the same set of beliefs (men as default human and women as "other", boys and men as having superior status and girls and women inferior status, girls and women existing to be exploited by boys and men, the normalisation of male violence and rape culture, etc, etc[.
One of the main pillars of patriarchy is the idea that it is the natural order rather than an ideology and a socio-political system. And the bedrock of patriarchy as natural order is gender. Gender is the socially constructed notion that sex should determine social role and status. This complex, extremist and oppressive notion is simplified, packaged and presented to us "femininity" and "masculinity".
Another age old pillar of patriarchy is that boys and men are human and self-defining and girls and women are not boys and men and are defined by boys and men.
The tenets upon which transgenderist ideology are founded are ancient and deeply ingrained. Transgenderism has simply picked up these ancient tenets and run with them in ways that are new. And because the ways are new, lots of people have been hoodwinked into thinking that there is something progressive going on. In fact, nothing could be further from the truth; it's just a case of old dog new tricks. The tenets are exactly the same as before and are deeply regressive.
So, personally, I'm still trying to achieve what I always have been - the liberation of girls and women from patriarchy and thereby gender / sex castes / male supremacism. Nothing has changed for me. I am resisting gender just as I always have because it is a tool with which to subjagate girls and women. What we call transgenderism is actually just plain old fashioned genderism. It is genderism mixed up with queer theory, social media, experimental medecine, pornography, fetishism, lesbophobia and homophobia, woman hating and the tedious god complex that men seemed to have had since forever.
You might as well ask "what is the feminist movement trying to achieve?". Or an even better question would be "what has the feminist movement always had to resist?".