There are a total of 16 spirits which you can get in the game. Most of them are found in the northen part of the island and to get them you need to search and find them. You then must defeat them in a duel and it is random if they will join you or not so it may take several attempts. The following is a list of when they are unlocked.

Unlock Adhesive Explosive:
Starter at well

Unlock Jerry Beans Man:
Starter at well

Unlock Oscillo Hero #2:
Starter at well

Unlock Skelengel:
Defeat Kagemaru

Unlock Acrobat Monkey:
Defeat Kagemaru

Unlock Hane-Hane:
Defeat Bastion for the second time

Unlock Soitsu:
After Abandomed dorm events

Unlock Ebon Magician Curran:
After Abandomed dorm events

Unlock Star Boy:
Defeat Bastion for the second time

Unlock Babycerasaurus:
After finalists are decided in tournament

Unlock Beelze Frog:
After finalists are decided in tournament

Unlock Blast Asmodian:
After finalists are decided in tournament

Unlock White Magician Pikeru:
Complete game

Unlock Batteryman C:
Complete game

Unlock Batteryman D:
Complete game

Unlock Dragon Capture Jar:
Complete game

Complete the following tasks to unlock the corresponding titles.

Unlock Dropout Boy Title:
Lose 475 duels.

Unlock King of Duels:
Win 475 duels.

Defeat the opponent or complete the following task to unlock the corresponding effect.

Unlock Duel Coat:
Get from Crowler when you defeat him.

Unlock Hawaiian Shirt:
Get from Atticus when you defeat him.

Unlock North Academy Uniform:
Get from Chazz when you defeat him.

Unlock Academy Jersey:
Get from Fonda when you defeat her.

Unlock Black Uniform:
Get from Chazz when you defeat him.

Unlock Yellow Uniform:
Get from Professor sartyr when you defeat him.

Unlock Stuffy Collared Shirt:
Get from linking With Nightmare Troubadour.