How hard would it be to implement the iOS API on Android?

High-level class interfaces aside, Android and iOS have different architectural philosophies about things like data access, process control, resource organization and loading, and overall program structure.  Simply writing NSFoundation/CocoaTouch adapters in Java would therefore only get you part of the way there. The cross-platforms efforts that have gained the greatest traction ( and , for example) take a different approach: they use a common, platform-independent API that has per-platform extensions where necessary.  That avoids the problem of mapping directly mapping Android to iOS, and vice-versa, but incurs the cost of adding an entirely new API with the overhead of an additional abstraction layer.

Leaving the specifics of iOS and Android aside, I think you'll find that the answer's about the same in the general world of computing.  You can write platform converters that take an RPG application and port it to Java, or other similar things, but they're both a lot of work and of limited value in the end.  The only cross-platform development approach that's ever really worked is to build a single virtual platform or cross-platform library that you can run on multiple devices.  These platforms tend to have their own limitations, but they're undoubtedly more successful than the "make my native code written for platform X run on platform Y" approaches. Finally, writing native code for each platform usually has the best result, but with the obvious cost of duplication of code, maintenance issues, etc.

It would be a huge effort and the result would a leaky abstraction. That would render it rather useless for serious application development. There would likely be so many bugs, performance differences and functional differences between iOS implementation and Android implementation, that you still couldn't run exactly same application source code in both environments. For example, Java ME is a collection of APIs that are meant to be portable, but because there are several different Java ME implementations with different bugs and performance characteristics, writing complex Java ME applications is really really hard. Google Maps is probably one of the greatest Java ME apps out there and even mighty Google doesn't try to port it to every Java ME implementation/hardware combination.