Starting in Chapter 3, Luchs can begin trading items with frequenters of the Famille Inn. Luchs can only make each trade once upon starting a New Game, not a New Game+. Any trades made in any previous playthrough in a New Game+ will be locked out.

If you keep the Mystery Capsule obtained from Bart in Ch. 4, opt to not trade it with Trixie in Ch. 6, and keep in until the final chapter to give back to Bart, you'll receive Innocent Wish and unlock the Secret Achievement "Good Listener". This means if you gave the Mystery Capsule to Trixie, you will have to craft Innocent Wish to unlock the Secret Achievement instead.

If you have the Pink Fruit in your possession upon starting a New Game+, and give it to Lottie in Ch. 3, you'll receive Merciful Heart and unlock the Secret Achievement "Reliable Friend". The Pink Fruit and Jade Brooch are items in the Other category, and are always carried over in a New Game+.

If you fail to keep a Fool's Medal as one of the 5 items you carry over in your New Game+, you'll miss out on an AP Regen +2 that playthrough. You can always come back to it in the next, but then you'd have to kill a Super Mimic and have it drop one. You can Quick Save prior finishing it and reload it until an item is dropped from it.

Any entry that begins with [???], is bolded, and is italicized is unconfirmed, but was Google Translated from the Japanese wiki.

Chapter Character Trade Item Reward
Ch. 3 Lottie Antidote Ruby Hairpin
Ch. 3 Trixie Mini Mixture Epsom Salts
Ch. 3 Bart Tin Mask Revitalize Bottle
Ch. 4 Day - Lottie's Chosen Trixie Ruby Hairpin Mineral Salts
Ch. 4 Day - Trixie's Chosen Lottie Epsom Salts Yggdrasil's Tear
Ch. 4 Night Frieda Revitalize Bottle Magnetite Shard
Ch. 4 Night Bart Yggdrasil's Tear Mystery Capsule
Ch. 6 Night Ingrid Revitalize Bottle Purple Neckalce
Ch. 6 Night McLaglen Magnetite Shard Amber Ring
Ch. 6 Day After Lottie Magnetite Shard Raw Magnetite
Ch. 6 Day After Trixie Mystery Capsule Panacea
Ch. 6 Day After Frieda Mineral Salts Master Mixture
Ch. 7 Lottie Panacea Yellow Button
Ch. 7 Bart Master Mixture Gustav's Horn
Ch. 7 Trixie Raw Magnetite Magnetite Ore
Ch. 8 Day 1 Lottie Purple Necklace Protein Drink
Ch. 8 Day 1 Trixie Amber Ring Legendary Spear
Ch. 8 Day 1 Frieda Gustav's Horn Gravity Bomb II
Ch. 8 Day 1 Gabbie Yellow Button Emerald Barrette
Ch. 8 Day 1 Bart Magnetite Ore Pure Magnetite
Ch. 8 Day 2 - Gewalt Leaves Di Legendary Spear Empty Shell Case
Ch. 8 Day 2 - Gewalt Leaves Fran Protein Drink Red Brooch
Ch. 8 Day 3 - After HEART Event Trixie Gravity Bomb II Mega Mixture
Ch. 8 Day 3 - After HEART Event Frieda Emerald Barrette Silver Gauntlet
Ch. 8 Day 3 - After HEART Event Gabbie Pure Magnetite Hero's Medal
Ch. 9 Day Lottie Hero's Medal Magnetite Gem
Ch. 9 Day Frieda Empty Shell Case Exercise Ball
Ch. 9 Day Addie Red Brooch Legendary Shield
Ch. 9 Day Trixie Silver Gauntlet Alpha Engine
Ch. 9 Day Gabbie Mega Mixture Massive Mixture
Ch. 9 Night - Post Party Trixie Magnetite Gem Claiomh Solais
Ch. 9 Night - Post Party Di Legendary Shield Jade Brooch
Ch. 9 Night - Post Party Fran Exercise Ball Pink Fruit
Ch. 9 Night - Post Party Bart Alpha Engine EXP Upsurge
Ch. 9 Night - Post Party Lottie Massive Mixture Abyss Fragment
Final Day 1 Frieda Abyss Fragment Fool's Medal
Final Day 2 - After HEART Event Bart Mystery Capsule Innocent Wish
Ch. 3 - New Game+ Lottie Pink Fruit Merciful Heart
Ch. 3 - New Game+ Trixie Jade Brooch Range +3
Ch. 3 - New Game+ Bart Fool's Medal AP Regen +2