I haven't completed any of the Wizard goals yet (with my skills, I was surprised I was able to even complete any of the Basic ones!), so I don't know what the description of the trophy for the Wizard completion will be. Probably [Table Name] Wizard.
when u complete the basic goals, wizard goals descriptions unlock, u can see them where u can see the basic goal descriptions, and if u completed any wizard goal before u complete the all basic goals it wont count as you complete the wizard, u have to do them after complete all basic goals.
for arabian nights table hardest wizard goal is rescue the princess, others are easy goals like extra ball or get ruby etc.