Read the FAQs. In lieu of, read this.
Yes, it's possible to work in Japan without a bachelor's degree. Here are the visa options:
1. spouse visa (marry a Japanese)
2. dependent visa (marry a foreigner who had a work visa)
3. student visa (enroll in school here)
4. cultural visa (study a craft under a master)
For 2, 3, and 4 above, you will have to file for special permission to work, and you will only be allowed PT hours.
5. regular work visa (but you have to prove a minimum of 3 years of work experience in a related field)
6. working holiday visa (you are not eligible because it is for certain nationalities and ages, and you don't fit either)