B.Sc

Yes with your B.Sc. in Zoology and M.Sc. in Animal Behaviour you are eligible to appear for the UGC NET exam. The UGC NET exam is conducted by the National Testing Agency (NTA) on behalf of the University Grants Commission (UGC) for determining the eligibility of candidates for the role of Assistant Professor or for the award of Junior Research Fellowship in Indian universities and colleges. 

To be eligible for the UGC NET exam you should have completed a master's degree (or its equivalent) with at least 55% marks (50% for reserved categories) in the relevant subject. As you have an M.Sc. in Animal Behaviour you fulfill this criterion.

In addition to the educational qualification there are other eligibility criteria such as age limit and nationality that you need to fulfill. You can check the official notification or website of UGC NET for more details regarding the eligibility criteria and application process.

No, there is no offline method of application. All the students must apply through the centralised entrance exam's official website, i.e., the official websites of CUET UG and CUET PG exam. After the COVID years and after the introduction of CUET UG and CUET PG for admission to Hindu College and other DU-affiliated colleges, the application process has shifted full-time to the online mode. Candidates can register on the official websites of the respective exam, fill out the online application forms, pay the course-wise application fee and appear for the exam to become eligible. For final admission, shortlisted and pass-out students of CUET UG and CUET PG are required to register on the DU CSAS portal for the final admission and seat allocation process.