Powering Up

Basics

Powering up is a little complicated, but it all centers around using Tech Points to increase your characters' stats. When I first saw that you could use tech points to increase your stats, I completely ignored it. I mean, when you can use your tech points to increase the speed and power of your tech attacks, why would you waste them to increase a stat by one point? And if you only do it once, then it won't make much of a difference. However, if you do it consistantly, after a bit of time your regular attacks will become more powerful than you old tech attacks.
So, use tech points to increase stats. Simple, right? Not quite. Namco had to go and make it a bit more difficult. You see, there is a cieling on how high each stat can be raised using tech points at a given time. This cieling is determined by the highest value of that stat among all your characters. For example, if KOS-MOS has the highest ether attack in your party, and it's value is 38, then your other characters will only be able to increase their ether attack to 38.
This brings up the topic of getting your characters "in sync"- getting your characters to have the same stats as each other. When this is achieved, you'll want to stagger your characters' experience so that each character levels up at a different time. This can be achieved by either killing party members before the end of a battle, so that they recieve no experience, or moving them out of the party so they only recieve %75 of the experience. Killing off party members has an interesting quirk you can read about in the Notes on point, and experience distribution after battle section. Then, after a battle when one of your characters levels up (and their stats increase), you can use tech points to increase the stats of all your other characters, so that they are all back in sync. In this way, when one character levels up, it is as if all your characters leveled up, but without getting closer to the level limit of 100.

Increase Those Tech Points

This requires a lot of tech points, without a lot of experience, because you need to obtain the tech points to increase your stats before you gain a level from experience. If you gain the level first, your stats will increase to the cieling value of those stats, and you will be unable to use tech points to increase the stats again. A waste of a level up, wouldn't you say? There are four ways to increase the tech points you earn, without increasing experience.

Only engage in battles with enemies that have a high TP/Experience ratio. Some enemies simply give you more tech points than others. Purposely battle enemies that have a good TP/Experience ratio, repeatedly. Avoid battles with enemies that have a low TP/Experience ratio. If you're strong enough to take on the next boss, you can totally avoid monsters with low TP/Experience ratios by using escape packs or Shion's ether, Goodbye, to get out of battle when it is impossible to avoid entering battle.
Use the point bonus in the event slot during battle. If possible, only destroy an enemy while the point bonus is active. Wait, if necessary. If one of the enemies is at critical health, boost when the "BG (boost gauge) Increase Rate Up" slot is active, so your character will have the next turn when the point bonus slot is active. When Shion learns the ether "Boost", use it to give your characters a boost if necessary. If you do this, you'll more than double the amount of tech points you gain.
Find those swimsuits! When a character is wearing a swimsuit during battle, they get 25% more tech points. Much to my lamentation, KOS-MOS can't wear a swimsuit >_<. Not only can she not get the TP bonus, but you can't see her in a swimsuit... Ziggy can't wear one either, but I'm not exactly excited to see a 98 year old male cyborg wearing a swimsuit, so I'm not too upset. Anyway, there are three swimsuits in the game, just the number you need ^_^.
1. The first one you get from beating level 4 in the driller mini-game.
2. The second (and easiest) one is in a treasure chest in sectors 46 and 47 of the Kukai foundation.
3. The third (and hardest one) is obtained from battling Great Joe onboard the Durandal.
Extract the skill from the swimsuits, and use the skill to double the effect of the swimsuit and get an overall 50% increase in tech points. Unfortunately, it requires a skill level of five, and a thousand skill points to extract, so you won't be able to take advantage of it until late in the game. But, KOS-MOS and Ziggy will be able to extract the skill and use it, so that's a plus.

Choosing Characters

Ideally, you should do this with all of your characters. That would yield characters with a virtual level of 600 after they have reached an actual level of 100, becuase with each level, it is as if they gained six levels. However, this is impossible. First of all, you don't always have all six characters in your party. But that doesn't really matter, because second of all, there just isn't a way to get enough tech points, without getting too much experience, even if you follow all of my advice. That is due to the fact that characters who don't participate in battle (and thus don't recieve any tech points) still gain %75 of the experience.
In the beginning of the game, I think that it is only reasonable to try and sync up three characters. But which three characters? There are three factors to look for in deciding which characters to use.

Early point of availablility
High natural stats
Can wear a swimsuit

I'm currently working on tables to show the natural stats of all the characters, so I can know for sure which characters have better natural stat growth. For now, I will follow what I've heard.
Shion is a definite, because she is always in your party, is available from the beginning of the game, and has decent stats. KOS-MOS, while unable to wear a swimsuit, is my second choice because I know she is avaiable at the start, has really high starting stats, and I've heard she has better stat growth.
I've heard that choas has high stats, so I'll choose him over MOMO. I don't really consider Ziggy, because he can't wear a swimsuit. And Jr. appears late in the game, which makes him an unattractive option.
So KOS-MOS, Shion, and Chaos are my suggestions, but feel free to try other combinations if you like.

Priority of stats

You will most likely be unable to sync your characters in every stat- it just takes to many tech points. So which stats should be increased when you have limited tech points? Some stats are cheaper to increase than others. I'm currently working on tables to show the cost of upgrading each stat. For now, I will determine priority based upon usefullness of the stat. Here is my recommendation:

Ether Defense
Vitality
Ether Attack
Strength
evasion
Dexterity
EP

The defense stats are first, because nothing else really matters if your enemies deal you zero damage when they attack. After your enemies start dealing you zero damage, I suggest moving the attack stats up in priority. Who needs more defense than invinceable?
The attack stats are next. More damage equals faster battles.
Evasion and dexterity are next. I put them low priority because I think they max out at 99- which means it gets pretty close to reaching the maximum without putting any tech points into it. Even if your enemies deal you zero damage, evasion is good because it will avoid status effects. Dexterity is below evasion because you usually don't have a problem hitting the enemy.
EP is last. I recommend only spending points on EP when you have extra points to burn. You generally have enough EP, and if your stats are high enough, you won't have a reason to use ether very often anyway.
"What about HP?"- you say? Never spend tech points on HP- it is obviously way more expensive to increase than any other stat, and besides, when your vitality and ether defense are really high, there is no need for a high HP. If you find yourself with enough points to Sync up with all other stats, and you still have more points, switch that character out and start syncing up another character.

Notes on point, and experience distribution after battle

Each enemy has a set number of experience points, tech points, skill points, and ether points that it gives for being defeated. If it is defeated during the point bonus of the event slot, the tech points, skill points, and ether points that it gives for being defeated are multiplied by 2, 4, or 10, according to the multiplier displayed on the screen. At the end of battle, all points given from the different monsters are added together, then divided equally among the characters who participated and survived the battle. Characters who died in battle, and weren't revived before the end of the battle recieve no points whatsoever. Characters not participating in battle recieve %75 of the amount of experience points recieved by the surviving characters of the battle, but recieve no tech, skill, or ether points. After tech, skill, and ether points are divided equally among surviving characters of the battle, modifications due to swimsuits, skill aprons, and their corresponding skills, are applied.
One point of interest is that the less people who are left standing at the end of battle, the more experience characters who did not participate in battle get. For example, let's say a particular battle pays out 100 experience, and 10 tech points. If three characters participate, and all survive, each of those three characters will get 33 experience points, and 3 tech points. Characters not participating in the battle will recieve %75 of the experience points, which is 24, and none of the tech points. If only one character survives the batle, that character recieves all 100 experience points, and all 10 tech points. Then the characters not participating in battle will recieve %75 of the 100 experiece points, which is 75 points, that's a %200 increase from before! And, of course, the characters who died in battle recieve no experience nor tech points. Now let's say that you have all six characters. When all three characters survive the battle, the total experience of your party increases by 33*3 + (33*0.75)*3 = 171, and the total tech points increase by 10. If two of your characters die during battle, the total tech points of your party still increase by ten, but the experience increases to 100*1 + (100*0.75)*3 = 325, a %90 increase from before!
So what does all this mean? Well, if the three characters participating in battle are the only characters that you wish to have in sync before you reach level 100, then this is a good thing. It means you can quickly increase the levels of players not participating in battle by killing off your own players before the end of battle. If you alternate who the surviving player is every so many battles, the three battle characters won't be affected, but non-battle characters will recieve three times the experience. While you can purposely use this as a strategy, it doesn't appeal to me, because it would mean having to take more time to plan the end of the battle, and having to heal my characters whenever I wanted to alternate the surviving character.
However, if you want to eventually sync up more than three characters, it means that ending battles with less people is bad, because all characters not participating in battle get closer to level 100, without getting any tech points that they will need to get in sync with the other characters. It is also bad if one of the characters that is in sync is not participating in battle, because that character will get levels quickly without getting the tech points needed to get back in sync before the next level gain.