you can unlock some costumes for your characters in 2 ways
-beat their story mode
-play missions

Mogar:Beat Story Mode With Irwin,Grim,Billy or Mandy

Eris:Beat Story Mode With Irwin,Grim,Billy or Mandy

Nergal:Beat Story Mode With Irwin,Grim,Billy or Mandy

Fred Fredburger:Beat Story Mode With Irwin,Grim,Billy or Mandy

Dracula:Beat Mission 5 on Tier 3

Lord Pain:Beat Mission 9 on Tier 5

Jack:Beat Mission 9 in Tier 2

Hoss:Beat Mission 9 in Tier 1

Boogey:Beat Mission 9 on Tier 4

General Skarr:Beat Mission 6 on Tier 4

Viking:Beat Story Mode With All Characters and Destroy Every Letter In The Credits

Nergling:Beat Story Mode With All Characters

Clown:Beat Story Mode With All Characters and Do 100 Vs. Mode Matches

Chicken:Beat Story Mode With All Characters and Do 10 Hours of Gameplay

Pumpkin:Beat Story Mode With All Characters and Do a Total of 100,000 of Damage