Chrono Trigger/The Queen Returns

Chrono Trigger > Chapter 2: The Queen Returns (600 A.D. first time)

Main Walkthrough
After taking a bold trip into the unknown, you'll be ambushed by a set of blue imps. They should die with one hit even on low levels, and continue to the left to enter a mountain area with a couple chests. You'll get into one more mandatory fight, and you can fight a couple blue imps kicking a ball back and forth. This will probably be the first fighting you do in the game in these areas, so use tonics if you need them, and rest in the inn or at the castle to keep your health up.

One thing to keep in mind about monster fights in general is that virtually all of them are strictly optional. Meaning if you're fast, careful, or just take the time to avoid them you can skip most of the "random monster" battles most people associate with RPGs. If this is your first run through the game I'd recommend fighting all the regular monsters just to build some levels, but if this is a New Game + you can practice dodging all the monsters. One general tip that comes in handy is that if you stay perfectly still monsters won't bother you, you have to be moving to engage them in battle.

Walk around the town, and while you won't know the year at first, someone will soon inform you that it's the year 600 A.D. and Guardia is at war with the mystics. Whenever you're ready, head into Guardia forest, and make sure to get the power tab at the bottom right area. You can also explore one of the bushes to grab a shelter.

Explore Guardia castle if you like, you can restore your health in the knight's quarters to the west, or the kitchen to the east. Eventually you'll want to head north, talk to the king, and head to the north east to visit "the queen." You can talk to the chancellor before or after you visit the queen, he'll say slightly different things.

Anyway, head upstairs, and you'll find out that Queen Leene is actually Marle. She'll thank you for coming for her, then suddenly disappear. Lucca will show up and explain that Marle is actually princess Nadia, and that Leene is her ancestor. Leene was going to be rescued, but they called off the search now that Marle was found. The problem is if Leene is never rescued, Marle will cease to exist, so you and Lucca head off to rescue her. You can talk to a few people in the castle for clues or Toma in the bar. Make sure you grab the bronze mail in the king's room before you leave.

Challenging Lavos
Impossible during this stage of the game since you have no access to a time gate.

Continue to Chapter 3: The Queen Is Gone (600 A.D. first time)