Explanation:

Correct option 2: was a meat-eater

Let's analyze the sentence:

"A new research study has shown that long before they took up a strict vegetarian diet, the much loved pandas was a meat-eater."

Let's break it down segment by segment:
1. "that long before"
– Grammatically correct. This is a valid clause starter. -------- No error

2. "was a meat-eater"
– The subject here is "pandas" which is plural, but the verb "was" is singular. 
Error: It should be "were a meat-eater" or better: "were meat-eaters"

3. "has shown"
– Correct tense for the present perfect referring to a study's finding. ------ No error

4. "took up"
– Simple past tense used appropriately. ------------ No error

Error Segment: 2. was a meat-eater

Corrected Sentence:
"A new research study has shown that long before they took up a strict vegetarian diet, the much-loved pandas were meat-eaters."

Final Answer: 2. was a meat-eater