If there are any internal guidelines on what to do, read them (they may or may not be helpful, but you should at least know what it says, if it's there.) Is there anyone else there who has been through it, whom you can ask for advice, how they did it?
At our place, there are functional and leadership capabilities and guides about what you're expected to achieve at each level, learning, competent or excellent. The higher you go, the more should be able to do as excellent; also your functional capabilities will change, so as you become more managerial, you gain more capabilities about supervising others and lose some of the technical stuff, as your day-to-day role doesn't expect you to maintain the same level of technical expertise.
So I have been working on showing I can do more than is expected at my level, and some of what should be done at the next level, giving specific examples as evidence. I think even if you don't have explicit specifications or a recent job spec, you should still have a good idea of what is expected of you in your current role and in the next level up, and find evidence of how you can fulfil those requirements, particularly things which show you using your initiative, leading others, solving problems, not having to be told and directed what to do. Anything that has improved efficiency and/or saved money is particularly good to highlight in most organisations.
I'm not actually expecting to get a promotion, but if they say, "you're not good enough, because..." then that should feed my dev plan. What I am more expecting is something like, "very good, but we can't have any more senior engineers in the department." What I really want is recognition that I am one of the best in the department, rather than being written off for not being male, not being German, and for speaking up when I see better ways of doing things, which useless male German manager then takes as a personal attack because it's not his idea...
As a general rule, I would say if you have a manager with people management skills that make a cardboard box look competent in comparison, you probably should just go elsewhere, but I have various reasons for not following my own advice for now.