Breaking it down literally.
First: "Anything" has no constraints. It is like infinity; it means everything from every place and then some. We live in a finite universe, at least for the moment. Even if the universe is infinite, in the absence of an ability to prove that, our universe as defined by "do" is finite. Minuscule, even. Put simply: This statement cannot possibly be true, unless you are omnipotent.
Second: From the first we have gotten, "I would do anything I am capable of." Would you? Would you really? Even setting aside the vagueness inherent in what you can and cannot do--at the present time or ever?--how many people are honestly promising to do anything they can, without heed to any other promise, any other moral or physical obligation?
Third: So you've decided you do mean you will do anything within your power, and that the person you're speaking to recognizes that stuff you literally cannot do is excluded. Having come to that conclusion, I must give you a warning: you only get to make this offer once. If you would do anything, the being may ask you something that will take the rest of your life, or will have ramifications you cannot foresee. And you will have promised. You must say yes. If you make this promise twice, it is a lie. If anything conflicts with fulfilling this promise, you must drop it, so making it twice means that if they ever come into conflict, you are screwed. And this is true for everything. For the rest of your existence. And choosing to end your existence is also a violation. You might be needed, and are avoiding your obligation.
Of course, that doesn't mean you can't make the offer. It just means that you don't want to have this on your list of things to blurt out, and that if you do blurt it out, you should be wary about taking it from offer to promise. In other words, backpedal fast and hope.