Just what the description says: Beat all
MISSIONS with all characters. This does not include Soul Attack or Episodes.
There are 28 missions total. There are 19 characters (you do not need to use every version of Ichigo for each mission). Simple math tells us:
28 (missions) x 19 (characters) =
532 missions to complete in order to obtain this trophy.
Sound grindy and arduous? Your damn right it is. This game takes about 100 hours to complete, and the bulk of that time will be spent either doing all 532 missions, or maxing every character. And with most characters you need them a high level prior to tackling the latter missions (26, 27, and 28). The one obvious exception is Kenpachi (I completed missions 28 with him at level 150 without any problem whatsoever).
All the missions are fairly straight forward, with some putting in various handicaps (no ignition gauge, no dash, etc). Because each mission has to be completed with everyone, there really isn't a simple way to go about this: you literally just have to dive in. I will offer some general pointers, however, to those that wish to plan their strategy ahead of time.
1.) Missions 1 - 12 are all fine for whatever level your respective characters is currently at. For example, taking Ulquiorra into mission 3 at level 1 is not going to cause you any serious headaches, so levels up to mission 12 really do not matter that much. However, getting to mission 12 you
should be at a relatively higher level (~50).
2.) Mission 13 is a pain just because it is a 1-hit kill for both you and the enemy. Unfortunately there are quite a few more enemies than you. I advise prior to this mission getting everyone the double jump and 1 life stock - this will alleviate A LOT of stress with this mission.
3.) Missions 14 through 22 are all fairly straight forward. 14 has you fighting Yammi, and you can't use ignition on this one, so you will be utilizing most characters triangle moves. Mission 18 removes the dash, however is is still fairly short - the only character that is annoying to run through this with is Aizen (because the dude walks like an old lady

) but for the no-dash missions with Aizen, just double jump: he glides a lot faster than he walks

.
Mission 19 is LOOOONNNG. 4 areas to roam through. And it is timed. And ignition gauge is not usable. And you have to fight Aizen and Gin at the end. Fun stuff. Prior to this mission your characters
SHOULD be around level 100.
Mission 22 some people will find annoying (as I did). The air recovery is disables, so when an enemy lands a hit you fall down, and it takes a while to get back up. It wouldn't be so bad if they didn't make you fight the top 3 Espada at the end

.
4.) Missions 23 - 27 is where the devs realized they were being complete sadists and decided to cut us a break

. All of these missions are fairly short, and since you should have been gaining crazy points prior to this you should be up in the levels dept. The only taxing mission of the bunch is 23 because, yet again, the dash is disabled. Fortunately it is not long at all.
5.) Before attempting mission 28, even on normal, heed my advice:
MAX MOST OF YOUR CHARACTERS. This will rid your experience of any unnecessary stress.
Mission 28 is comprised of 10 stages with nothing but boss battles on each stage:
STAGE 1: Rudbone, and some Menos that spring up.
STAGE 2: Barragan and a couple of hollow spawning baddies
STAGE 3: Yammi
STAGE 4: The guy with the fox face (I can't remember his name

) and 2 elite guards
STAGE 5: Ulquiorra, Grimmjow and Ichigo (Bankai)
STAGE 6: Ishida, Kokuto and Hollowfied Ichigo
STAGE 7: Nnoitra, Kenpachi, Kyoraku and Stark
STAGE 8: Soi Fon, Yuroichi, Rukia and Halibel
STAGE 9: Toshiro, Gin, Byakuya and Aizen (Awakened)
STAGE 10: Aizen (Final), Barragan, Kokuto and Ichigo (Final)
On normal 2 stages will be a problem: 8 and 10. On 8 you NEED to take out Soi Fon - she will two-hit drop you and remove a life stock. Focus on her first.
On Stage 10 you need to get rid of Aizen in a hurry - he is a cheap bastard that will grab you and take a good half of your life without warning.
On normal difficulty you do not need to worry about the enemy spamming their ignitions like they do on Very Hard, but if you see a boss use their ignition for a second time, then they will use their ultimate attack, so be warned.
That is all I can think of for right now. If anyone has a any questions regarding a specific mission let me know in the comments below.