The Steam version may have been rebalanced, but with the SNES one early on you pretty much just have to hit things. Your two girls use Strike - so Hit ring rather than Power - and the men use swords and such. Ayla uses Power though:-). It isn't so wrong to just hit something as soon as possible, like whenever the timer comes up then quickly hit... whatever you can. As you get better weapons, and especially when you get magic, you'll want to hold off and think a bit more, especially at the configurations like if Lucca drops a bomb over here, then Chrono should not hit here too but rather over there, etc.
One thing that might have thrown you off is that Sewer area. You aren't meant to go there just yet! It can be done, but man is it tough! One way is to go forward, get Robo, and use him for extra power. Plus that next area has weapons for everyone. Another is to wait until you have magic. Or you can grind before and just tough it out, but anyway there's nothing really at the end of it, it's just EXP and treasure and fun and adventure - but best saved for later.:-)
One trick: when you gain the ability to travel through time at will, you can bring in a healer, heal everyone, then ditch them again. I usually use Robo for that bc he's so damn slow (agility) that I don't like using him in battles. This saves MP. Early on that very first forest area has a secret spot where the bushes wiggle and when you click a monster pops out and runs away - no battle necessary - and it gives you a tent. You can get basically unlimited of those by leaving and coming back:-).
You need very limited grinding in this game. It's possible to use none, but then there would indeed be certain battles that would be much tougher. Maybe do every area twice or something. If you decide early on who you want to use, you can focus on them to get the highest levels. But you don't know all the combo attacks yet - like Chrono + Lucca + Princess can do several spectacular magic attacks together, they are quite a versatile team. Frog is great too especially if you get his secret items but that would be better as another playthrough with a guide. Ayla is great and doesn't even need items, just lots levels. At some point you'll lose access to all your items you'll want her to be not totally neglected. So basically: rotate them all in occasionally, until you know what you are doing. Did you know they get ~75% of EXP even when left behind? But they don't get AP. There is a particular enemy that locks down your skills that gives you 100 AP for beating it, and there are only a few in the game, all in pretty much one area (looks like a rock that woke up) - that's what you want to be strategic about.
But you discovered the caveat to the above: early on is when Chrono needs his slash skill the most, to hit those things that are immune to a physical bonk attack. The way I always did it was to take him through the forest area at the start of the game, or flight the carnival robot, but those were optional and if you didn't, a few levels could really help. Or try to avoid those battles except they spring up on you so that's not something you'll know about in the first playthrough. One thought: that sewer area can get hairy fast, but if you go in, flight a few battles, go back out and save, repeat and go a bit deeper, etc. it would give you a ton of EXP, plus neat items like Rage belt that auto-counterattacks. That's my favorite pick for Chrono bc he'll get so strong that he'll kill things outright just by letting them hit him!:-P
Yeah just before where you are, that was the boring part - though you are close to leaving the future and that's exactly when it picks up! Like, literal magic isn't far away now!:-) I'd put a berserker onto the Princess, for now until she gets magic, which will also help with deciding what to do bc she'll auto-attack then, with greatly increased ability, and go through the last dome with first her to the right and then Lucca to the left (bc of fire). Then almost never use the robot again, except for healing outside of battle, and a few other times it makes sense as well, and he can be fun then:-).
The final boss can be as difficult or easy as you want. In-game tips on a few secret areas are given but extremely cryptic. Worth figuring out though bc e.g. getting hit with confusion can wreck any strategy, while being outright immune to that makes it so much easier:-). You can also decide which characters to bring, or not bring, and that affects the ending sequence that you'll see.:-)
Oh wow you have so much awesomeness ahead of you - enjoy it!:-)