Can you help me find a GBA Fire Emblem Hack that fits my needs?

As far as I recall mGBA doesn’t have those filters. If you must have filters perhaps you should use Retroarch. You can install the mGBA core in it and apply filters to whatever you are playing.

While in the game open the Retroarch in game overlay, go down to Shaders → Load → Shaders slang. There are multiple folders within which each have multiple shader options which you may find to your liking. xBRZ, Super Eagle, and HQ2x that Yasako mentioned are all there.