I don't want to harp on balance concerns too much as the currently-locked Spells button suggests we're missing an entire game mechanic but yeah, success right now seems heavily reliant on RNG with very few opportunities to turn a weak start around due to the low number of events per run.
Your best bet is to focus on getting dealt a starting skill set that can attack any spot without being too costly, can attack multiple targets, or can assist with crowd control. You can do full attack damage regardless of color zone with cheap skills like Power Thrust which can also move targets around, and a lot of the movement skills can also do extra collision damage if you bump enemies into each other. Ninja and Archer's skills feel much more useful than Swordswoman's to me so far, as a bunch of her skills are restricted to her attack zone, and non-offensive support skills have rarely worked out for me due to the heavy cost, and the opportunity cost of not being able to carry a more versatile skill in the slot.
The second piece of the puzzle is items from events, many of which can enable any heroine to attack any spot for 20 damage, which bailed me out of more than one tight spot. Pick whatever path is going to get you nice stuff.