There are 20 unlockable characters, I will cover 4 in each part

Shopkeeper (Spend 1500 money): Make a custom character with cash as a starting item, spend it all, then click "End Game", repeat until you get the shopkeeper

Red Gangster (Kill 10 Blue Gangsters): Play multiplayer with one person being a Blue Gangster (more Blue Gangsters will spawn) and the others being classes with high killpower (Soldier Demolitionist (DLC) Custom etc.), find & kill 10 Blue Gangsters as the high killpower classes

Bartender (Drink 10 alcoholic drinks in a single game): Create a custom character that starts with money, beer, whiskey and 4/4 on the "Speed" stat, get damaged, drink the alcohol, use the money to buy more alcohol, repeat until you unlock the bartender, recommended that you have a second player act as a bodyguard, or a second beer-drinker

Scientist (Poison 5 air-filtration systems) Play as a custom character that starts with a syringe and 4/4 on the "Speed" stat, find an air-filtration system and put it in, then end the game and repeat, you can speed up the process by waiting for the syringe-gas to disappear then using another player with another syringe

These characters can be hard to unlock without skill/planning

Gorilla (Rescue a Gorilla from a cage): Play as either The Hacker or someone with killpower, find a caged gorilla (normally in a science lab) and either kill all the scientists and get the key or hack a computer and open the door (depends on who you're playing as)

Cop (Bribe 3 cops): Play as a custom character that starts with money, find and bribe a cop, either end the game or complete the floor and bribe another cop (if you think you have enough money left), repeat until you've bribed 3 of them

Vampire (destroy 20 graves in a single game): Play as a character with the Ghost Gibber (or someone who's really fast), find some gravestones, either use the Ghost Gibber or run if any ghosts appear, finish the level or when you finish destroying the graves, then find more graves and repeat until you unlock the vampire, I recommend using the "infinite ammo", "infinite durability", "continue" and "no patrolling cops" mutators for this one

Wrestler (complete slums using only fists): Turn on the "No Guns", "No Melee Weapons" and "Continue" mutators then go into the slums with a custom character with 4/4 strength (you could use ECTD to give yourself more strength), punch your way through everything (easier in Multiplayer) until you unlock the character

This part is a bit of a mixed bag

Assassin (complete anyfloor without killing/alerting anyone): Go as someone who can knock-out people without killing them (like the doctor), go to the slums and activate Solid Snake mode, complete the slums and restart if you kill/alert anyone (the end of a floor will give you XP for not killing/alerting anyone), this one might be easy if you're good at Metal Gear or any other stealth games, Alternatively you can let your friend/a 2nd player fully clear the floor, then just teleport to the exit and go to the next floor, credit to Geecko for this alt unlock strategy

Comedian (Get a kill with a banana peel): play as a custom chartacter with 1/4 endurance and a Banana as a staring item, get hurt and use the banana to get the peel, damage yourself until you're on low HP (about 5 or so), step on the banana peel and die (you can get the character by killing yourself with the peel)

Jock (Complete a floor with a destruction level of 75): Play as a character who can cause mass destruction (Demolitionist (DLC), characters with RPGs etc), destroy building and use multiplayer to progress faster and complete floors easier (IDK how you get destruction level)

Shapeshifter (Complete any floor with 5 non-custom characters): Probably the easiest one, Play through the slums normally with 5 different normal characters, you can use mutators like Infinite Ammo to make this easier

These characters have some... interesting unlock conditions

Investment Banker (find 500 coins in a single game), Create a custom character with 8 starting items (and some negative traits if requited), sell the items until you have 500 coins, use multiplayer to make this easier

Werewolf (Kill a ghost): Use a character with a Ghost Gibber, destroy graves until a ghost appears, kill the ghost

Cannibal (Complete a floor with 20 killed): Go to the Slums with the soldier and the "Infinite Ammo" mutator, commit genocide then complete the floor normally

Slavemaster (Buy 4 slaves): Play as a character that starts with money, go to a slavemaster and buy a slave, End Run and repeat until you get the character,you could make this faster by using multiplayer or buying multiple slaves in 1 run (if you think you have enough money)

2 of these are character specific, the other 2 are easier with custom characters

Zombie (Complete slums with Vampire): Pick the vampire and go into the slums, play the game normally until you beat the slums, a way to make this easier would be to get a freeze ray (Those machine things, the guy at the base, etc) and turn on "Infinite Ammo", then you could freeze and SUCC people to regain health

Firefighter (extinguish 5 fires in a single game): Create a custom character with a flamethrower and fire extinguisher, burn something then immediately extinguish it, repeat until you unlock the character (Use "Infinite Ammo" and burn something different if you destroy something by burning it)

Mobster (Bribe a mobster to influence the mayoral election): Play as a character that starts with money, go to the slums or industrial and earn more money, get to Downtown and find a mobster that won't kill you, give him the money and he'll influence the mayoral election and you'll unlock him

Robot (Hack a Cop-Bot/Killer Robot): Play as the hacker (I recommend having other players as bodyguards), either turn on all of the "Disable ____ Disaster" mutators except "Disable Killer Robot", play to floor 3 then find somewhere safe and just hack the robot, or spawn Cop-Bots in some way and hack them