So I've been playing Fire Emblem Heroes for quite a few days, and its been quite hard trying to beat the levels I am at now. World 9 with like level 23+. It sucks because the opponent usually has the field advantage but beyond that. I have to put myself at a disadvantage because the opponent will not move. Is there any tactic to make it so that I will have a better chance succeeding or do I just keep going to the tower, grind and then play until my units are better.
What I tend to do when I have disadvantage, is set up an attack. The opponent won't move until you are in a danger zone (most of the time), which can allow you to organize your units in a way that will allow first strike capabilities. Ranged units are especially good at achieving this. Mounted units as well.
Granted, after this first strike... it's up to how well you are set up. If your team is all flying and you are up against archers, well... it might be time to hit the training tower and reorganize your team.
Much like you say, world 9 is where the game starts posing a challenge(it did for me as well anyway), and you need to start organizing teams and units accordingly. Unlocking Potential can also help very much, once you bring them back up to strength afterwards.
Rapitor's answer is excellent, but I think it should also be noted that setting up units to defend against attacks can be an even more powerful strategy than getting first attacks in some situations, especially when your team is less mobile or has less range than the opponent.
A great example of this comes when pitting your Robin (M) against an enemy Takumi. For most stat distributions, neither of these characters will be able to one hit KO each other. If Robin gets the first attack against Takumi, each character will take a bit over half damage, and the enemy will be able to finish off your Robin without further damage. If, however, you place Robin just at the edge of Takumi's attack range (and out of range of anyone else), Takumi will attack Robin, they will each take a little over half damage, and you'll be able to finish off Takumi on your next turn.
When you start a map with a disadvantage, especially if it's a map where the units don't move until you enter their range, I've found that the strongest strategy is to find a map square that only one enemy can hit and place a unit that's strong against that enemy there. You can move your other units around as much as you want to set up an offense/defense before you trigger the battle. Once you trigger the battle, all the enemy units will move toward you, and you can then have your rear units start picking them off.