I don't have time to write up a full guide, but do have enough info to summarize the process.
Difficulty: 3/10 Time: 50 Hours Playthroughs: 3
Trials of Mana - Your shiny Platinum and named after the game itself. In the words of Elliot, "Ooo! Wow!"
Heroes of Mana - Defeat the new bonus boss that becomes available in a path after defeating the main final boss. (Fun fact: Heroes of Mana is the name of this game's direct prequel as well.)
Mana Sword's Chosen - Play through with all six characters. They do not have to be the main character. Can be done in 2 runs.
Laurentian Guard - Individual character trophies that contribute to Mana Sword's Chosen. Can be done in 2 runs.
Adventure's End - Story-related trophies for progressing through the game. Unmissable
Throw Money At It - Requires 5,000 Lucre to immediately purchase Nitromyte from Watts in Dwarf Tunnels. You can grind for it on a first run or wait until NG+ when you have more money than you'll ever need.
Ruler of the Seas
Winged Defender - Story-related and will trigger the first time you use various new travel methods. Unmissable.
Treasure Hunter - Simply open every chest you find to get to 100/200 overall. I do not know if progress carries over to NG+, but you'll easily hit 200 before unlocking NG+.
Wealthy - Accumulate 100K/500K lucre. This is NOT cumulative and you must have it on hand all at once. You'll most likely hit this before opening NG+ if you're fighting every battle after no longer needing to buy weapons. Selling extra gear from Rainbow Item Seeds ramps up your funds too.
Extreme Power - Continue to invest Training Points in your characters and these will unlock eventually. It may be best to wait until the 3x experience boost in NG+ to go for the final one as you'll likely unlock NG+ around Level 80 and it basically requires being at Level 98-99 to have enough Training Points. Note that is is just all abilities for one character, you do NOT have to get all of the Chain Abilities from NPCs.
Power of Bonds - Automatic after speaking to the Priest of Light in Wendel. Unmissable. Other Chain Abilities can be learned by speaking with people important to a town/character but are often dependent on who your main character is (or is not. For example, you get one from Duran's mother in his house, but only if he's not in the party because he refuses to return home).
Bonds of Allies - Learned after unlocking any party member's first Chain ability. Will come naturally unless you're intentionally not building your characters.
Chosen One - Defeat the new post-game bonus boss on Hard. Difficulty can be switched at any time. You can go for this on your first run or save it for your final one before Platinum when your NG+ team is maxed out. There are also challenges for defeating Anise on higher difficulties under certain time limits. But you just have to beat her on Hard once for this trophy.
Glorious One - Defeat the final boss with Duran or Angela as your main character.
Immortal One - Defeat the final boss with Kevin or Charlotte as your main character.
Overcoming Reality - Defeat the final boss with Hawkeye or Riesz as your main character. These three are what require the three full runs and, if you beat Anise on Hard ahead of time, your 3rd one of these will most likely be your last one before Platinum.
Rabite Trapper - The Black Rabite becomes available after clearing the final dungeon before returning to the Sanctuary of Mana at the very end of the game. Return to the final dungeon and there will be a rabbit statue that warps you to a previously-inaccessible area. The Black Rabite is the original game's super boss, so come prepared. Unlike the original, it can be found on every route and is no longer missable.
Ultimate Guard - Get each of the characters to Class 4 in post-game. Requires a minimum of 2 runs.
Power Hungry - Upgrade your class at a Mana Stone at Level 18. Most easily done at the Wind Stone since it's the first available and, even on a fresh file, you'll be close to Level 18 upon arrival if you fight nearly every battle.
Cactus Colleague - The first encounter with Li'l Cactus is unmissable. He'll be found on the Golden Road after leaving Maia.
Cactus Companion - Perhaps the most difficult trophy in the game as Li'l Cactus has 50 different spawn points. None of them are missable and here are a few rules of thumb:
* He can be found once in every town that you have access to at the end of the game.
* He will appear at least once in every dungeon, twice in larger/repeat dungeons (usually Mana Stone/Benevodon dungeons), so keep a sharp eye out.
* He does NOT appear in any of the final dungeons (Dracomaw/Mirage Palace/Dark Castle), but will be found twice in the dungeons preceding them (Crystal Desert, Jungle of Visions, Night Cave)
* After getting 35 stamps, you gain the ability to see how many appearances he makes on each map.
* When you're on the overworld map, you can press up and down to filter icons. Make sure Show All Areas is on to get the quickest view of which ones still have Li'l Cactus sightings (after getting 35 stamps).
Gardener - Plant any seed. Easy peasy.
Horticulturist - Plant every seed you get and constantly pick up shiny objects on the ground as they will likely be a cheap item, lucre, or seeds. If you haven't maxed out your Item Pot at Level 5 by the end of the game, you'll more than likely get enough to max it out by the time you defeat Anise.
And, finally, here's what I know about New Game+
* Most Items, Lucre, and learned Chain Abilities carry over. Plot progression key items do not.
* Li'l Cactus rewards/progress and (I'm pretty sure) Item Pot level carry over. You can get a bunch of Gold/Rainbow/??? seeds from the bonus dungeon after maxing out your Item Pot and carry those over to chance getting the best gear for your next team early on as well as items needed for Class 3
* Just to be safe, unequip any gear you want to carry over into NG+, especially if you plan to re-use a same character/class.
* Starting NG+ unlocks Chain Abilities for Faerie and the 3 characters you beat the game with. Fairie's grants a 300% experience boost if you want to breeze through the game.
* Character levels carry over into NG+. So your third run will be cake.
* Save your Gold/Rainbow Item seeds until reaching Class 3. You won't get the best gear possible from the seeds until then. The uber-rare gear won't unlock from seeds until Class 4, but the Class 3 stuff is good enough for post-game.
Enjoy the game!