Tracing is the best way. https://www.romhacking.net/documents/361/
is for graphics and for vba-sdl-h (no$gba debug has since become free and is rather more graphical than command line, however tracing works much the same on all systems -- break on read, break on write, break on value being greater than or less than or equal to being rather similar concepts in all systems).
Find the enemy health value (fortunately games like this have one, as opposed to one hit and done type games) as per standard cheat finding methods, and if you know how to sort luck you can probably nerf attack to do one damage each time and give yourself plenty of search opportunities. As multiple enemies can exist in one screen/room it may be multiple values/an array but that is nothing major and will likely be similar between screens so go for a one enemy room if you like just to make life easier.
Upon said health value reaching zero many things will happen, one of those will be figuring out item dropping. While I say many (death animation, handling of a health bar, kill counter increase, experience, souls... I can't remember all the mechanics for this one) it is probably enough that you could go by hand if you had to as for most of those you need not know how they work, just enough to know what they do and then dismiss them in favour of your main target.
Possible bonus. http://datacrystal.romhacking.net/wiki/Castlevania:_Aria_of_Sorrow_%28Game_Boy_Advance%29:ROM_map
I know it is the other GBA entry but... let's just say few would argue Konami GBA and DS peeps were not fans of code reuse. To that end what is there is probably largely going to be similar to what you will see there and you can then look for similar structures. The split between drop rates for common and rare likely going to crop up here as well (it is an easy way of simplifying your drop algorithms), and may even take luck into account a different way.
Also worth noting. If there are any items that influence drop rate you might find some value there, however the health thing is probably quicker and a lot of drop things in games tend to be flags rather than some kind of mechanical advantage. On the other hand the only thing reading said flag if you can find it (equip and unequip is not so hard and can make for a decent cheat search) will be the drop algorithms and thus you can possibly even search for anything reading that memory location (or set a breakpoint for said same).