1. When you come to a new level of a dungeon, scout around as far as you can go, opening as many of the bridges and lowering as many columns as you can until you need the pioneers. Kill all the CIMA that don't spawn from nests, find all the safe rooms and good vantage points to keep CIMA from hurting the pioneers. If you know the terrain and what you're up against, it will help minimize injury to your characters. And once you open the way to a new segment with the pioneers, get them to a safety area and repeat this step.
2. Pass the Heal Ring among the wounded! It saves time and Majesties, since barring a few circumstances when you're up against sniping CIMA and have to stay on a switch a long time, each individual won't suffer too bad an injury. If you use the last tip, you'll have several points when you can recover safely, and you get two of them pretty early. The Potion Cs you find can take care of the few times this strategy won't be useful.
3. When leveling your characters' weapons and armor up, a good checklist of what to do is...
A: Get Ark up as high as possible, since he does the most fighting.
B: Get all characters up to 2 added Defense points and 2 added Offense points (the latter is only applicable if said character has a weapon). That way, characters can better care for themselves in puzzle situations.
C: Get the four group leaders in the last dungeon (Vanrose, Doug, Rick and Jean) up as high as possible, so they don't die horribly against their respective bosses (especially Jean...his can be hard even with the upgrades if you're not careful).
D: Distribute remaining points as you see fit. You might choose to power up the defense of the weakest members (i.e. Telmia, Ileyda and Emmy for defense, or even extra for Halley's second-lowest HP), or give your remaining fighter characters more offense (Halley, Shelley and Ivy) to protect the non-fighters in splits if their AI decides to fight back. Some might decide to simply concentrate on Ivy first since she's with Ark most of the time and does lead the group from time to time.
Note that you can get enough Materials to Upgrade everyone fully, and can find their locations in my Dungeon guide, but if you miss things and don't feel like going back for them, or just don't care to get the more annoying ones, then this order is best.
4. If you go to the back of the Blue Creek, your characters will come out and tell you how much they trust Ark. It changes as your Trust gets higher, starting when you just hit positive, with new ones at 30, 60 and 100. At 100, they have a special convo, where they show their Trust for you (i.e. Doug wishing Ark had been there 20 years earlier, Philis finally getting the courage to tell him how she feels or Rick planning to name his child after Ark).
The one funny thing with these is that there's no affect on the story in any way. Doug will show his anger at Ark until after Lonely Factory even at 100 Trust, while Halley and Emmy will be the Gate Guardians' biggest fans even when they're in the negatives. So seeing the conversations and getting to 100 Trust isn't a necessary part of the game to better your party, however it's still a nice touch. The only change that Trust gives to your game is being able to synthesize items at the positive levels, and having a cushion in case the character gets attacked so they won't fall down to negative ones.
5. If you don't care to see all of the conversations, then there's a way to do most if not all of your Trust farming in the first dungeon. In the previous article, I briefly mentioned a CIMA nest you could use to get characters to positive Trust after the big dropoff during the encounter with Pike. While you can use it to simply get your potion makers (Jean and Eberle) to a base positive, thus being able to make Potion As cheaply as soon as you get them to gain a surplus for early in the game, you can also position the entire party outside the nest, attacking until everyone is at a positive level. The downside is, due to their low Base Trust, getting Vanrose and Doug to positive levels will mean that most everyone else will be pretty high up when you finish. So you can either do the minimum for potions if you care to see all the conversations, or the maximum to get a high trust for your party without endless farming when you get people. Or even stagger the groups coming to the switch so people start hitting positive around the same time.
6. Here's a list of places where you can fight the easiest enemies in the game, spawning from nests endlessly on the first floors of dungeons, to get each of the different types. The places listed are the earliest possible ones you can use after finishing Beginning World...
Rectangles: Rogs, first level of Silver Snow, near the entrance. You could also choose to kill the Piyon there to hopefully get another.
Diamonds: Grabions, first level of Lost Forest, near the entrance.
Stars: Vanices, first level of Lost Forest, back near the exit room. You need some pioneers to stand on the switch to get them closer. Also, destroy the monsters around the room so they leave you alone.
Spheres: The earliest possible place would be in Dragon's Dungeon, in a nest shared by Dria and Rogs. However, it's not the most advisable due to the fireballs, so I wouldn't suggest it. Instead, stock up whenever you find a nest with Sphere dropping enemies in dungeons. This is another reason for the great Wog-slaying Trust-farming of Beginning World, you can start with a sizable cache.
Later in the game, at Air Garden, you can fight Fasguns for them on the first floor, however they are defensive (it took me two hits to kill them with Ark's Level 4 weapon) and are located past many popping up Poyons, an inconvenient Bobyn nest and a Temptus shooting at you from the sidelines of a platform directing a timed gate...making it not advisable to slog the pioneers if you're coupling Trust and Majesty farming. If you can wait to Twilight World, however, you can fight Byunos near the entrance; they may be more defensive, however they're not past anything dangerous sans the spikes and you can just keep the Byuno off the switch so nobody gets hurt walking there.
All in all, there is really no convenient place to farm for Spheres easily, just places to get them if you're in dire need.
7. Remember to recheck your group settings every time A) a character joins the group or B) one or more characters are separated from the pack. Especially in the latter case, because even if you set the person you know will be teleported to being in a large group, they may completely reorganize in ways that don't make sense and someone might be left alone (happened to me once. Doug was with Eberle, Emmy and Philis, and when he was caught in a Teleport Trap somehow everyone was pushed forward and Yurald was left alone for an entire floor cuz I didn't realize the mistake till we were on the move).