Can't say I have done Z80 with IDA but the idea of beating IDA is kind of similar to a lot things we see in forums like this that use the word "just" (as in "just" disassemble it and rewrite it in C). IDA is a seriously powerful tool and though I doubt its z80 capabilities are as good as its X86* (my usual suggestion for a sort of primer on X86 IDA is http://www.youtube.com/watch?v=a7vTTspWcTE
) I imagine it is around what its ARM abilities are at.
*if nothing else embedded single program on simple processor vs full OS and X86 security will make sure there is not even the potential.
To that end you are going to need at least
Disassembly, basic static disassembly is obvious. Ability to assign nice names to memory locations is also necessary, you may or may not wish to include logic far enough to handle pointer maths in the disassembly)
Instruction generation. Single instruction and small run. You can kick full code to an external assembler. Back on nice names thing I will be wanting pointer maths type things with my nice names.
Code injection help. Free space finders are hard, especially if you are already dealing with MBCs, but such things are available for embedded processors. However if I tell you something is free space and the location of my jumps/returns then I would like that sorted.
Code running. Obviously this is not full emulation, though the ability to speak to BGB or something, even if you just snatch the memory out of the program's memory space on the PC would be nice. However the ability to set register values and run the routine and spit out results will be sought.
Maybe some kind of bounds checking. The GB/GBC memory map is pretty full but not entirely, you might also try to code in a warn if a read/write/injection goes beyond the thing it looks like it is fiddling with.
Back on the disassembly you are going to want almost full IDE (or at least notepad++ level) where you can section off things (this is my [blah] function, this is not running code....) and have a nice minimise button to shrink it down.
IDA is a serious tool, there is a reason they can ask for and get paid the good money for their tools. More generally a lot of it is just nice to have, I would focus less on beating IDA (for my next trick....) and more on getting what you reckon is useful in there.