I'm currently doing Masters in environmental sciences. Can I do law practice with having only a Diploma in environment law & not LLB or LLM?

No, you cannot practice with a Diploma. You need to have a LLB Degree in order to practice. Most places, including private and government require you to have a LLB Degree. However, certain paralegal work or research based work may be hiring people Diploma holders. But, full time lawyers need to have