More gameplay mechanics than character design:
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Giant characters that are actual giant characters as in they take up more than one square on the map. So you can have a giant character that takes up a 2x2 square and who can travel twice as far as normal 1x1 square characters per turn. To balance this out, they have 0% dodge (and can't critically dodge) and can't fit in narrow 1 square pathways. They also take cumulative damage for each square hit by an aoe spell, so if an aoe covers the entire 2x2 square, they take 4x the damage as a normal character would.
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Characters that affect terrain. So like a sapper character that tunnels through impassible mountains, engineer character that builds a bridge/raft on bodies of water, a pyromancer that turns a forest tile to a plains tile (lore explanation is them casting a fire spell to burn the forest), geomancer that spawns a mountain to box enemy troops in.
I don't know how feasible this would be for what you're trying to do. If you're talking about creating a ROM hack for a GBA FE, I don't think you could do this. Maybe you could have an aquatic/amphibious class that has massive movement bonuses on water but take massive movement penalties on land. I think the pirate(?) class in one of the GBA FE can walk on water, so maybe you could do something there where you give the character a natural high movement value but give them massive movement penalties on any terrain that's not water. I think having a mermaid character or even a fish character is pretty out there for a FE game since those games mostly take place on land. But you don't necessarily have to have every battle take place in an open plain, a castle, or a cave. You could totally have sea battles in an SRPG.