Stages B-1 to B-3 cleared
That is not a mispelling, to earn this trophy to have to clear B-1, B-2, and B-3. Before you can clear these stages you have to unlock the stages.
Unlock Stage B-1: obtain the "secret service" trophy
Unlock Stage B-2: obtain the "Ladies' Man" trophy
Unlock Stage B-3: obtain the "shachihoko" trophy
Letter of Thanks
Stages 1-1 to 4-X and B-1 to B-3 cleared
Stages 1-1 to 4-X, then B-1 to B-3 cleared. Just need a simple clear, nothing special.
Secret Service Company
All VIPs rescued from stages 1-1 to 4-X and B-1 to B-3
Rescue all VIPs for Stages 1-1 to 4-X and B-1 to B-3.
Launched fireworks on all stages from 1-1 to 4-3 (excluding extra stages) and B-1 to B-3
This is a little tough, you have to get fireworks on Stages 1-1 through 4-3 and B-1 to B-3. Take heed, you need to get the fireworks before the rescue ship gets there.
Rescued Professor Poseidon and his wife
Find Professor Poseidon on 3-1 and his lovely wife on stage B-2.
★★★ achieved on stages 1-1 to 4-X and B-1 to B-3
You have to get a three star stage clear on stages 1-1 to 4-X and B-1 to B-3. To get a three star stage clear you need to earn a certain amount of points to do this. In order to get the points you need to get ALL VIPs and make the chain equal the number of survivors needed for the stage clear.
Here are the stage scores needed for Three Stars Clear!