Alcohol and tobacco are two hazards to health; they harm our body.
Does the underlined part sound right to you? Thanks.
In such a generalized statement, QD, (especially with the use of "our") you should go with the plural "bodies".
I also think that you should qualify "health" ie: "Alcohol and tobacco are two hazards to
good health". Just using the word "health" doesn't seem quite right. If you reworded your statement and said:
"Alcohol and tobacco are unhealthy", this denotes "bad" health. This is why I think your statement has to refer to "good" health.