So yeeeh, let's brainstorm about goal concepts?
Destroy Supplies: This involves, basically, targeting a specific class of units and counting their deaths. For a "destroy supply" mission, you would utilize enemy Transport tents or wagons. Another variant could be "destroy ballistae", for a map focused on the enemy's artillery tactics. FE7x implements this as a timed mission, which adds a bit of pressure. Original the chapter goal, property of YetiCorp.
Protect Villages for X Turns: Pretty self explanatory. Might be a way of spicing up that bland earlygame brandit chapter? FE needs more defensively-oriented objectives. The problem with Seize/Rout/Defeat boss is that they're basically all the same. GBAFE sparingly uses timed Survive maps. Utilizing the occasional "complete in X turns" for Seize/Defeat boss maps could also be another way of diversifying the goals.
Defeat X Enemies: We've seen something like this once before, in FE10. Pretty self-explanatory. Crazycolorz even coded it to work in GBAFE. Would love to see more of these in fan projects. Could give these missions a "guerrilla warfare" feel, even, based on the map design/enemy placement. FE10's map was basically a two-way slaughter where every death counted towards the total.
Open Chests: Let's go looting!
There are also a few under-utilized goals we've seen in the FE series that would be neat to see more of in fan projects.
Seize All Castles: The hallmark of FE4. It'd be cool to see a project adopt one or two of these larger-scale seize maps (FE4 prologue is about as big as you can get in GBAFE). FE4 used seizing as a means of linear progression; but having, say, a map with two castles to seize and whichever one doesn't get seized first responds reinforces themselves could be interesting.
Escape: As long as they don't basically turn into rout maps (ala FE9), I always love the occasional escape mission. FE5 debuted this chapter goal, and any unit that you left behind was captured by the enemy (you can't get them back until Chapter 21x; by which point said unit is vastly underleveled). Perhaps it might be better to take a page from FE9's playbook, and give units who escape a free level-up instead (well, FE9 gave BEXP but same idea). That way, you're incentivizing players to have everyone escape with a carrot, instead of beating them with a stick.
Let's hear everybody's wacky chapter goal ideas, or ways in which we can spice up the standard FE goals. Should be interesting!