At the End of Time, you choose to return to your own time, the year 1000 A.D.
If you want a free, one-time heal up, eat the cake on the table. However, if your health is full, leave it there so you can use it later.
Try to leave the house and there will be some dialogue. Afterward, leave the house.
Enter the Elder's House to the north. Take the Speed Tab from the table on the ground floor, then go upstairs and take the Magic Tab from the counter. Go outside.
Go west to Melchior's Hut. Buy equipment from him.
Now switch Marle and Lucca into your party.
Go north from Melchior's Hut and enter Heckran Cave.
Use magic on all the enemies in here, except for the two that attack you at the entrance. The path from the entrance is straightforward and leads to a chest (Ether). Go south from the chest and follow the path. When you try to go downstairs, a Jinn Bottle and some Octoblushes attack. After you defeat them, go down the stairs.
Defeat the Tempurites. From here, there is a west path and a south path. Go south first and follow the path to reach a chest at the end (MagicScarf), then go back and take the west path.
Open the chest (Mid Ether), then you will fight more Tempurites. Afterward, go north and open the chest there (Ether), then go south.
In the room after the area where you fight the RolyPolys and Cave Bats, you can avoid a fight by staying near the east wall. Then go through the north door.
Follow the path, and when you reach the save point, use a Shelter and save. Then go north up the stairs. Go north to start a boss battle.
While fighting Heckran, keep HP above 100. Use your magic attacks, but stop attacking when Heckran says "Go ahead, try and attack!" If you attack him when his claw is in front of him, he will counterattack. Wait until he says "Brief counterattack break" before you resume attacking.
Eventually, Heckran will always have his claw in front of him, even after he says "Brief Counterattack Break". It is safe to attack him after he says "Brief Counterattack Break".
Heckran Cave, Part 2
Go north and jump into the pool.
Take note of the spot where you land, northeast of Lucca's house: it's called "Vortex Pt." on the map, and if you go there and press A, it will take you back to the pool in Heckran Cave.
Before anything else, go into Lucca's house, go through the door, go up the northeast stairs, and wait for Taban to give money to Lucca's mom. Then go back to the first room and talk to Taban. You'll get an item for Lucca.
Now go north to the Market (in the group of buildings on the left) and if you saved the guy from the guillotine in the dungeon, you'll get a reward.
You can visit your mom to see a brief cutscene, then go upstairs and rest in Crono's bed.Next, go north to Leene Square, go north to the Telepods, and use the Gate. At the End of Time, use the northernmost pillar to go to 600 A.D.