essence shielding let you destroy the tower with the mages in the first section of the battle.
yhilin magic let robin speak directily with yhilin mage guild and prevent the guild go in "sieged mode"
the third research is the orc one.
for the stats, a 'good' result: nothing in the city is destroyed or otherwise damage, you don't need to spend any DF (Discretionary Funds, they are introduced after the battle and will replace the 'ProN' for investment in the whole chapter 3) in the recovery, this can be transalted in a chaos and CD score of 4 or less and the ability to null them with the works in the city after the battle. enemy army of 29 or less and 19 vicotry point. [there isn't any gain in go above 25 VP, but in the first iteration of yhilin you need to spend DF in a double noble support campaign for boost ambasador evaluation, this mean +6 VP, thus you need 19+ score, keep in mind some activity or dialogue grant VP, if you can do that and have the right rp score with some girl]
if you don't know
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it's a HTML calculator for BoY, for optimization without the need to do all math first hand.