To start of, character quests are the side quests that you get from the other members of the party, many of these quests have to be completed to play trough the game. You can see if a character quest is available either by the questionmarks above their heads, or by looking in your questlog under the "unlocked quests" tab. Every character has three quests.
If you have trouble with finding your destination, press the left stick and the game shows you where to go.
And here is the list of all character quests in the game, most of these shouldn't make any trouble. There will be spoilers in this list.
Jack:
1. The first character quest asks you to meet Choo Choo on the bridge as Rachel. You just have to go to the far northwest corner on a little island, after that answer a phone in the motel which is a little southwest from the island.
2. For the second quest, you have to find a protagonist's cure-all on the marketplace, just search a few objects and you will find it.
3. The third quest and probably one of the hardest in the whole game is Choo Choo's ultimate test. He will stand at the northern end of the bridge. This quest is just waves of all the different enemies in the game which you have to survive.
Rachel
1. You have to get her a zombie game from the mall, it's in the far northwest corner of the mall, just search the shelf and you get it.
2. This quest asks you to burn tyres. First of all you need the flamethrower which is the enhanced version of Jack's torch, you get the gas canister in the suburbia area. When you got it, combine it with the lighter. The tyres are right outside the room with the party members in the power plant (if you don't remember how to use the status changing tools, like the flamethrower, you hold LT and use RT to shoot).
3. For the last quest of Rachel you have to get a grow up potion for which you have to kill oversized zombies. Oversized zombies are just sonic-emitted zombies, just go to a police car and kill the sonic-emitted zombies until you have it.
Brian
1. Brian needs a fire mutant brain. Kill a fire mutant, to make one you have to irradiate and incinerate a zombie at the same time and hope that he transforms.
2. Here he needs a sonic mutant brain. It's the same as the first only that you need a sonic-emitted irradiated zombie.
3. And at last he needs a electric mutant brain. Same as above just with a electric charged irradiated zombie.
Luxo
1. First you need to get four letter blocks from the mall. Press the left stick if you have trouble with this.
2. In this quest you need to retrieve the comic from the locker in the power plant, it's located at the far left room, after you try to search it, you have to find the stolen key on the marketplace. Just kill electric zombies until the key drops and return to the locker.
3. You have to get a dvd from the tv station, use the left stick if you have trouble.
The achievement is flagged as buggy because it can unlock without meeting the requirements, so it's a positiv bug.
If you have any questions or improvements for the solution please say so.
I hope this helps.
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Daeryoon added:
A hint for surviving the Choo Choo mission: use the brains of the mutants as a way to freeze all the enemies. In the last wave, kill one mutant, go touch the brain, then kill another, and repeat. It should only take 2-3 shotgun shots to kill one from the back close range.
pynnokyr added:
The level 2 vampire shotgun made the choo choo quest a breeze, because it regains health through damage that you do and ammo shouldn't be a problem.