Character unlocks differs between the 3DS and Wii U versions. I'm posting a complete list for both versions below. Source

Ness

3DS: 10 Smash matches or beat Classic mode
Wii U: Unlocked by default

Falco

3DS: 20 Smash matches or beat Classic mode without using any continues
Wii U: 10 Smash matches or beat Classic mode

Wario

3DS: 30 Smash matches or complete 100 man smash
Wii U: 20 Smash matches or complete 100 man smash

Lucina

3DS: 40 Smash matches or beat classic mode as Marth without using any continues
Wii U: 30 Smash matches or beat Master Core (classic mode final boss at intensity 5.1 or greater) as Marth at 5.5 intensity

Dark Pit

3DS: 50 Smash matches or beat Classic mode with three or more characters
Wii U: 40 Smash matches or beat All-Star mode on Normal

Dr Mario

3DS: 60 Smash matches or beat Classic mode as mario at intensity 4.0 or greater
Wii U: 50 Smash matches or beat one Master Order on hard difficulty

R.O.B.

3DS: 70 Smash matches or collect 200 trophies then play a Smash match or beat classic mode
Wii U: 60 Smash matches or defeat Crazy Hand after completing 10 matches in Crazy Orders

Ganondorf

3DS: 80 Smash matches or beat Classic mode as Link at intensity 5.0 or higher
Wii U: Unlocked by default

Mr.Game & Watch

3DS: 90 Smash matches or beat Classic mode with ten fighters
Wii U: 80 Smash matches or beat Classic mode with five fighters

Bowser Jr

3DS: 100 Smash matches or beat Classic Mode as Bowser on Intensity 6.0 or higher
Wii U: Unlocked by default

Duck Hunt

3DS: 110 Smash matches or beat Classic Mode with 8 or more characters
Wii U: 100 Smash matches or KO one fighter in Cruel Smash

Jigglypuff

3DS: 120 Smash matches or collect 30 different equipment items
Wii U: Unlocked by default

DLC Characters

Mewtwo

3DS: $3.99
Wii U: $3.99
Both: $4.99

Lucas

3DS: $3.99
Wii U: $3.99
Both: $4.99

Roy

3DS: $3.99
Wii U: $3.99
Both: $4.99

Ryu W/ Suzaku Castle

3DS: $5.99
Wii U: $5.99
Both: $6.99
(Note: This DLC comes with the stage as well as the fighter)

Cloud W/ Midgar

3DS: $5.99
Wii U: $5.99
Both: $6.99
(Note: This DLC comes with the stage as well as the fighter)

Corrin

3DS: $4.99
Wii U: $4.99
Both: $5.99

Bayonetta W/ Umbra Clock Tower

3DS: $5.99
Wii U: $5.99
Both: $6.99
(Note: This DLC comes with the stage as well as the fighter)

Going by the example set by previous games, training mode defines a "combo" as "series of attacks that keep the opponent in hitstun", possibly with one frame of escape window (not sure as of this time). So, you need to get in 100 hits without allowing the opponent a chance to act.

Being that it's hard enough to get a legitimate combo of 20, you're going to have to cheat a little bit. Spawn a bunch of Smart Bombs and explode 'em. Depending on a few migitating factors, the resulting combo will be somewhere between 50 and 100. Give it a few tries and you'll get it eventually.

As for the "400 across everyone" challenge, that's an average of about 8 per character. The chunk of 100 will drive this down to about 6 per character, which is easy enough with a single Smart Bomb or even characters' infinite jabs.