After fighting through some high-powered aliens and getting Zexonyte, Dr. Andonuts is able to fix the Phase Distorter.
Give Dr. Andonuts the Zexonyte
Use the Meteorite piece on Dr. Andonuts in Saturn Valley (go to it in your inventory and choose Use). Then rest in the Saturn Valley hotel, and the Phase Distorter II will be ready in the morning.
When you go into the Phase Distorter II, you won't be able to go back. Make sure to prepare. Equip everyone with protection from Flash: the Sea Pendant from Magicant, the Night Pendants from the new Mr. Saturn in the Saturn Valley shop, and the Star Pendants that have a 1/128 chance of dropping from Major Psychic Psychos in Fire Spring, block Flash completely. Poo can equip one of these pendants for Flash protection, but the Cloak of Kings boosts his Defense and Speed more (but doesn't protect from Flash), so it is your choice.
Before you gather all of the things that you want to take with you, keep in mind that you should leave one space free in Ness's inventory, and one space free in someone else's inventory.
You should also get Multi Bottle Rockets in Deep Darkness, Super Plush Bears in Summers, and Brain Food Lunches in Dalaam. If you don't mind waiting three minutes each time, you can order Large Pizzas by calling Mach Pizza, since Large Pizzas restore 240 HP for everyone but Poo. Also, give Paula the Franklin Badge since she has the lowest HP, and make sure that she is equipped with the Sea Pendant, Night Pendant, or Star Pendant.
You might want to check what you have stored in Escargo Express in case you have been holding onto anything that you were saving for later. Now is the time to have your best items with you. For example, the Hand-Aid, Magic Truffles, and so on.
If you want to get every possible Photo Man picture, check the Photo Locations page. However, you will still have a chance to get more Photo Man pictures after this.
If Ness is level 75 or lower, level him up to at least level 76 before you go. This will make him immune from Homesickness. You can go to the cave beyond the Tenda Village and fight Fobbies in the upper floor of the cave to easily earn EXP.
Make sure Ness isn't Homesick, then talk to Dr. Andonuts when you are ready to go, then talk to him again to confirm that you are ready. Then walk into the Phase Distorter.
Arrive in the Cave
The Phase Distorter II takes you to the strange cave that you may have visited in the Lost Underworld. After you step out of the machine, you can check on it to call your Dad.
Go east, and the Star Master will teach Poo PSI Starstorm Ω.
Keep going east and you find a Mr. Saturn next to the broken Phase Distorter that Pokey stole. Check on the broken machine to get a Horn of Life.
Go north to look at the metal tentacle. It doesn't do anything. Go west to the end of the cliff, then go south and the Phase Distorter III will appear. Talk to Apple Kid, then talk to Dr. Andonuts. When he walks away, follow him and talk to him again. Say Yes to his questions. Then when you are in the Phase Distorter, say Yes to activate it and you will travel to the Cave of the Past.