What is your budget and worst-case timeline? You ask for ""highest possible"", but exactly this can take a very long time to optimize, a great many transistors in parallel, and large custom magnetics. Do you, in fact, have a budget or size limitation that prohibits achieving truly unbridled highest efficiency? Or is your actual requirement more like, there is some minimum efficiency you must meet, and given any other limitations, whether it is possible to achieve? Finally -- is the efficiency constraint actually driven by another constraint such as power dissipation and surface area? Like I said, the solution could end up quite large, in which case its power dissipation may be rather moot -- and then "highest possible" efficiency isn't actually required.
We also need to know all the usual power-related specs: input range, output range, source and load impedance, does it need to be fault-tolerant, how will it respond under transient conditions such as inductive surge or load short, how will it start up, is this from a battery, does it need precharge, is it precharging something else, does it need current limited output; what level of EMI filtering is required; what is the operating temperature range, is cooling water available if applicable, what contamination level (environmental dust, humidity, etc.) will it be exposed to, etc.
Also, I realize you quoted "highest efficiency", but is this quoting from somewhere else, a spec perhaps, an assignment? If so, please show what you can. Context matters; if this is merely a school assignment, say, then there is some expected amount of work, and at least the general form of it, or the approach, is "the correct answer". If this is for a work project, then it matters what it connects to, how it functions within the system; requirements are driven by that, and whatever efficiency you get, is what you will get.
And other than that -- perhaps you used quotes for emphasis? Sarcasm? Do you not actually need it at all, but then why ask? I'm inclined to take it at face value as you can see, but these are questions that are avoided by making a clear problem statement including all requirements.
And also not to sound like a nag, or some nefarious engineering genie looking for loopholes -- but tightly constrained engineering problems often do take the form of the proverbial genie problem, and it pays to think in terms of that. The lesson is, understand that there are a great many constraints that apply to even very simple elements of a system. Maybe, if you're having trouble with one of the parameters, consider others -- contemplate, strategize -- maybe there's something they missed, that does in fact constrain the other parameters more tightly, preventing an absolute statement; and now you can in effect "disprove" the given specification as impossible, and push back on the requirements and get something a bit more nuanced, and feasible.
Tim