The skill. I finally got it to level up: by fighting horribly outnumbered battles in person, like with any normal playthrough. 
I did not consider this strategy the first few times because the perks mostly seem to influence auto-calculated (or "simulated?") battles, so I incorrectly tried to level the skill using auto-calc. I also tried running away from fights a lot (sacrificing troops, etc), and only a couple of breaking-into-the-siege to help defend thing (again, sacrificing troops), all of which felt bad and wasteful, but still contributed a bit more to the skill than auto-calc battles. Oops.
(Being outnumbered by 2 or 3 to 1 seemed to increase the skill at about 100X the speed of the other methods)
My suggestion:
Do one of two things:
1) Make the skill go up a lot faster when auto-calc battles are done (this is what the perks are currently used for, anyways...)
Or, my preference:
2) Change the tactics perks to affect normal gameplay (you know... not auto-calc but actually playing through the combat and all). Just like the Minister of Health adds the +hit points to all your troops in all situations, the top perk in tactics should +% damage in more situations than just auto-calc.
(yes, I am biased: I generally don't like auto-calculating battles)
TLDR:
The skill feels odd compared to every other skill in the game: to get good at something you generally do that thing and not something else. This skill does not line up with its current perks and skill benefits
I did not consider this strategy the first few times because the perks mostly seem to influence auto-calculated (or "simulated?") battles, so I incorrectly tried to level the skill using auto-calc
. I also tried running away from fights a lot (sacrificing troops, etc), and only a couple of breaking-into-the-siege to help defend thing (again, sacrificing troops), all of which felt bad and wasteful, but still contributed a bit more to the skill than auto-calc battles. Oops.(Being outnumbered by 2 or 3 to 1 seemed to increase the skill at about 100X the speed of the other methods)
My suggestion:
Do one of two things:
1) Make the skill go up a lot faster when auto-calc battles are done (this is what the perks are currently used for, anyways...)
Or, my preference:
2) Change the tactics perks to affect normal gameplay (you know... not auto-calc but actually playing through the combat and all). Just like the Minister of Health adds the +hit points to all your troops in all situations, the top perk in tactics should +% damage in more situations than just auto-calc.
(yes, I am biased: I generally don't like auto-calculating battles)
TLDR:
The skill feels odd compared to every other skill in the game: to get good at something you generally do that thing and not something else. This skill does not line up with its current perks and skill benefits