How to Break the Difficulty of Chrono Cross Without
Cheating.
Step 1: Buy a lot of traps before the body swap. I usually buy 5 of each, with 3 summons. The summons aren't needed for this strat, but it's nice to have for later. I do this just before I enter Ft. Dragonia.
Step 2: Trap 5 of each of the following in Ft. Dragonia: Holy Light from SonofaGun (Blank face,) Inferno from Bunyip (First form.) There is several others that are handy (such as Gloop having Iceberg to trap,) but the red and white elements are valuable for an upcoming boss strategy.
--Remember, you can run away and still keep any elements you've trapped. It'll reset the fight, but you can do this until you have what you need and/or until you're bored. I'd still recommend 5 of the above mentioned elements.
Step 3: Trap 5 Ultra Novas from Mega Starky (when he's in critical) once you can get to him as Lynx.
Step 4: Start the "Save Marbule" side quest. When you are still a cat (er, a smaller cat) on the casino ship, you'll need to go to Nikki's dressing room and watch the scene between him and Irenes.
--Bonus! The Sage fight is your first chance to trap Deluge and Carnivore. Use the trap you want to start his attack chain for that color. His attack pattern will reset to back to normal once the spell (Deluge or Carnivore or whatever you're trapping) is cast. Beats waiting for the Green Dragon or the SideSteppas much later in the game.

Step 5: When you get to the Dead Sea, trap Volcanoes from the Tragediennes (those are the pain in the arse ghosts inside the Tower of Geddon. The ones with the overly long introduction.) If you want to bring someone other than Fargo for the Dario fight (like Draggy if you got him in Home World Ft. Dragonia) this will be handy.
--Bonus! They are great for trapping Black Holes and Tornadoes early on. It makes that long as hell introduction mostly worthwhile.
Step 6: Make sure to visit Home World's Earth Dragon isle if you haven't done so already. Get to the dead end, then talk to the NPC right next to the sand boil up top. We'll be back here in a few.
Step 7: Once you get the Dragon Relic fetch quest, immediately get Marbule done in the Home World and defeat the Black Dragon (she's in Another World.) Don't forget to have Fargo steal the Black Plate!
Step 8: Take care of Karsh's Level 7 Tech quest at the Isle of the Damned.
--Bonus! Steal from Solt to get the "Forget-Me-Not-Pot." Useless for the boss fights, but it's the first time you can get one before Chronopolis.
Step 9: Now head back to the HM Earth Dragon Isle. You should be able to proceed and kill the dragon. Don't forget to steal that Yellow Plate either!
You'll need it for the Sphinx! Otherwise, you are dead.
Step 10: Time to do the Dario quest, while using the Red Element Trick with a bit of a twist. My setup was:
--Riddel: Mythril or Stone Rod/Black Plate/Magic Seal/Sight Scope/Mythril or Stone Helm. Her physical damage sucks anyhow, so if you forgot to make a new rod for her, don't sweat it.
Stock her up with Ultra Nova (as many as you can, even down in the negatives,) Holy Light and others. A few healing spells is also there, but I try not to use them with her save for emergencies.
--Fargo: Stone Sword/Sight Scope/Silver Loupe/Dragoon Gauntlet. You'll want to keep him with high hit % and extra strength helps too.
He's not much of a caster, so he became my primary healer and buff bot. As a blue innate, he can use Cure All, which is very nice. He's got one of the Revive (set at elemental slot #2) spells you can get by that point in the game. For extra fun, throw Weaken on Dario and get Eagle Eye on Riddel.
I usually don't have him steal. The item and the counter attack (Weaken) isn't worth the effort. He's good for physical attacks otherwise.
--Lynx: Stone Swallow/Silver Loupe/Dragoon's Honor/Mythril or Stone Helm.
I gave him some more healing spells than Riddel, but loaded with all of the higher end Red Elements. He also has Revive in slot #2. If you're using Draggy instead of Fargo, give the red elements to Draggy and make Lynx the physical damage dealer and the party's healer.
--Riddel will get healed by ConductaRod when she casts her white elements. Lynx will only get Numble for using the Red Elements, Fargo is on heals.
--As long as Dario doesn't take out both Fargo and Lynx, just keep Fargo's elemental grid. Have him stick to physical attacks and heal if needed. If someone dies more than twice (or Fargo dying twice for example), just run away and restart the fight.
--Between Ultra Nova (which even at -1 was doing over 450dmg,) Holy Light and Inferno, he dropped in 5 minutes. Congrats, you're almost done kissing the difficulty goodbye in Chrono Cross!
Step 11: Lynx will need the Mastermune/Yellow Plate/Star Fragment or Yellow Brooch/Dragoon's Honor/Mythril or Stone Helm.
--Load up on Green Elements, strong Black Elements (since that's his innate) and healing. Head to Another World's Earth Dragon Isle.
--Bring along Fargo, but otherwise the third party member doesn't matter. Like with Dario this isn't worth a Star Level, but they don't need to live too long in this fight. They aren't really needed for this though.
Step 12: Start by having Fargo attacking the Sphinx instead of doing the riddle. Have him try to grab a Rainbow Shell. If not, don't worry about it. It's a rare steal and not worth restarting the fight for imho.
Step 13: The Sphinx will go apeshit and start spamming Earthquake and ThundaStorm. This is why the plate and the Star Fragment are needed for this fight. You can also trap up those spells if you feel like. I trapped Earthquake later on, and I've never used ThundaStorm much outside of Gaia's Navel, but it's up to you.
--His attack pattern goes: Earthquake -> ThundaStorm -> Earthquake immediately followed by Thundastorm->Attack x3 ->Earthquake (rinse, repeat)
Step 14: Beat the snot outta him with physical attacks, then pop off the green element (or black, since that works well.) When he does that standalone ThundaStorm, break up the field to where it isn't all yellow. Defend when he attacks. Heal if needed, but you'll get healed once the Sphinx starts his magical attacks.
Step 15: Rinse and repeat until it's dead.
Step 16: Equip Serge/Lynx with the Dragoon's Honor, the Sunglasses and a Power Seal.
Congratulations, you've killed most of the difficulty in the game! With that set up, 250-400 dmg right out the gatewith a fierce attack, everthing is very easy from here on out. With the Mastermune's high crit rate, you do a crapton of damage per hit.
Even the Dragon God is easy. Enjoy!
--Bonus! If you want to use the Viper Dragoon Glory glitch, put two of those on Serge plus the Sunglasses. Then proceed to cackle with maniacal glee.
I usually get 8 (three for the companions and two for the main character, since I never take off the Sunglasses on Serge) plus 10-12 more just for the cash. You'll still need a Specter Swallow for the NG+, and the gear itself is
pricey. I did this because I didn't want to farm for cash as long in Chronopolis. Again.