How do you unlock the Bowser board and those two weird looking characters on Mario Party 8 for wii.

First you have to get up to Bowser's Warped Orbit in Star Battle Arena then you will VS Hammer bro. After that, you will have to get up to Bowser's Warped Orbit again and then you will VS Blooper. Try and beat him and then try and beat Bowser and then you will unlock him. Good Luck!

beat the star battle arena once to unlock stage (bowser's warped orbit) and blooper to unlock hammer bro beat the star battle arena twice.

Defeat Star Battle arena to unlock one of the unlockable characters, and then use the character you just unlocked to beat the Star Battle Arena again to get the other unlockable character.
(This response may be late but I'll say this for anyone else who needs help)

You have to go through all the party boards to unlock Bowser's board.And you get Hammer Bro if you go against him then you need to go against Blooper if you want to unlock him in Bowser's Party Board.