In order to win at Tower of Trials, you first have to have three decently strong girls. They need to at minimum be three stars, and preferably girls who started at one star and you've ranked up from there. In the talent tree, max out both the star rank and level of the first skill you get for all three girls.

Your first opponents in Tower of Trials will be weaker than you. But if they take half of your life, that's no good, as your life doesn't refill from one match to the next. Rather, you need to make sure that you have elemental or class advantages for just about every single duel. Most of the time, you want to plot out which of your three girls will duel which of the three enemy girls. Sometimes you'll want one of yours to fight two of theirs. But plan it before you start the battle rather than scrambling wildly in battle.

Set the combat type to assisted attack and don't use any skills for the first few battles unless you have to. The only skill you want to ever use in Tower of Trials is your first one. Start the battle with your preferred matchup advantage against the enemy's first girl and try to win with just you basic attack. Once you do and the enemy sends in his second girl, click on your preferred matchup against his second girl to switch. Make sure you switch a little after your opponent does, as dropping a new girl on him seems to do substantial extra damage. And then again for the third girl.

When you win a match, all of your surviving girls that were on your team for the match get a substantial health and SP refill. In the early matches, you want to use this to accumulate a lot of SP, as your SP doesn't get reset from one match to the next.

Whatever you do, don't let any of your three main girls die. You probably don't have a good replacement for her, and even if you did, it would wipe her accumulated SP. If you use your first skill to deal damage, you're invulnerable while the skill plays. In some cases, it won't actually deal that much damage, but you don't take any damage at all while it plays. If you get into trouble, either switch girls or spam that skill to slowly wear down your opponent without taking further damage yourself.

As you go to higher floors, your opponents get harder. You can sometimes end up fighting against yourself on floors seven or eight, which are the ones where your opponent is about as strong as you. But you still get to choose the matchups for elemental or class advantages. Also importantly, by the time you get to higher floors, you should have a lot of SP accumulated. If you need to, that might let one of your girls beat an enemy with 30% higher power than her basically without taking damage by burning through accumulated SP to spam a skill.