Hint: Play Deumantis
You may normally play as the third Deumantis after you are defeated. Clear the game once and you'll get the option to choose between the two characters.
Hint: Unlock More Characters
Play survival mode using the two enemy characters in the upper right character selection menu to unlock hidden fighters (such as Ultraman Noah). Play the character in the bottom of the middle row (the scorpion like monster) to unlock the third Nexus.