This absolutely doesn't have to have an ultimatum flavor about it. The whole point of any conversation on the topic is that you have goals that you'd like to meet. I think it's a great conversation to have with your manager. Here's my recommendation:
Establish your why
This keeps your "goal" from being a finishing line. Why do you want to advance? What purpose will you drive and serve while climbing the ladder? Please don't say "I want to make more money" or something similarly vapid. Money is the by-product of pursuing a deeper "why". Why do you want to achieve these things? How do they benefit other people more than just yourself? To potential commenters: When I defined my why, I decided I wanted to produce the best software possible in whatever space I worked in. As an individual contributor I can only produce so much. By moving into leadership, I can help 5, 10, 50 people achieve that goal.
Establish your milestones (metrics)
This is more than just simple targets. There are milestones that define that you're progressing in your career: "Became a manager", "Became a director", etc. These milestones are good, and they should be taken into consideration. What other milestones do you have? These would be skills you learn, accomplishments you want to achieve. These milestones tell you that you're growing the right way not just achieving status.
Establish your timelines
Goals without timelines and metrics are just hopes and dreams. When will you have done some of these things? How will you know it's done? How will you know it's done well?
Enlist your manager's support (get them involved)
Ask for your manager's assistance in refining each of these things. When it becomes a collaboration between the two of you there can't be any form of ultimatum. If they're involved in the solution, they'll also be invested in your progress, and that will help during the course of achievement either through motivational assistance or potentially through material assistance. This might take the form of them approving a training class or a management program.
Track your progress
Ultimately, you need to keep track of your progress both good and bad. You need to be able to demonstrate to your manager (and their manager) that you're valuable and making gains for the entire organization. Then in the end, if you're not valued or advanced in the manner that fits your goals, you'll have a mighty fine resume at your disposal. It's not an ultimatum at that point. It's just the natural next step in the journey.