Here's how you unlock the various characters:

Andy- --

Max- --

Sami- --

Olaf- --

Grit- Beat mission 5 (Sniper!) and then finish campaign.

Drake- Beat the four Green Earth missions (Captain Drake, Naval Clash, Wings of Victory!, Battle Mystery) with Andy, then finish campaign.

Eagle- Beat the four Green Earth missions (Captain Drake, Naval Clash, Wings of Victory!, Battle Mystery) with Sami, then finish campaign.
Then beat the secret 'Rivals!' mission.

Kanbei- Complete campaign.

Sonja- (Phew) Beat the three Yellow Comet missions like this:

Kanbei Arrives! in 8 days or less (I managed 5!)
Mighty Kanbei! in 10 days or less (I got 9...)
Kanbei's Error? in 12 days or less (I got 10)

Then beat the secret Sonja missions, and finish campaign.

Hire Sturm- Get the characters above.

Nell- Finish Advanced Campaign.

There's how to unlock all the characters...