No. Those who teach that baptism is essential for eternal salvation, are preaching a Works-based false gospel, wherein human good works are believed to contribute to one's Salvation. But the Bible is very clear that Eternal Salvation is a Free Gift of God, devoid of human works.
There are 2 types of baptism mentioned in the Bible.
Baptism of the Holy Spirit is the indwelling of the Holy Spirit received by every true believer at the very moment of Salvation. This is not a special experience for a group of so-called super good Christians.
Ephesians 4:5 - "One Lord, one faith, one baptism"
Acts 1:5 - "For John truly baptized with water; but ye shall be baptized with the Holy Ghost not many days hence."
Matthew 3:11 - "I indeed baptize you with water unto repentance: but he that cometh after me is mightier than I, whose shoes I am not worthy to bear: he shall baptize you with the Holy Ghost, and [with] fire:"
Water baptism can be taken by a believer, publicly identifying himself/herself in the body of Christ and the family of God. But, this is not an essential duty for receiving Salvation.
The verse that is often misunderstood to teach water baptism as a requirement for Salvation is John 3:5.
“3Jesus answered and said unto him, Verily, verily, I say unto thee, Except a man be born again, he cannot see the kingdom of God. 4Nicodemus saith unto him, How can a man be born when he is old? can he enter the second time into his mother's womb, and be born? 5Jesus answered, Verily, verily, I say unto thee, Except a man be born of water and the Spirit, he cannot enter into the kingdom of God. 6That which is born of the flesh is flesh, and that which is born of the Spirit is spirit. 7Marvel not that I said unto thee, Ye must be born again. 8The wind bloweth where it listeth, and thou hearest the sound thereof, but can not tell whence it cometh, and whither it goeth: so is everyone that is born of the Spirit.”
The water mentioned in the above verse does NOT mean Water Baptism.
Verse 6 explains what the "water" in Verse 5 is. It is talking about the normal human birth- the birth in the flesh.
Also, "water" is used in many other places in the Bible, where it does not mean "water baptism" but the "living water".
"I will sprinkle clean water on you, and you will be clean; I will cleanse you from all your impurities and all your idols."
"But whoever drinks the water I give them will never thirst. Indeed, the water I give them will become in them a spring of water welling up to eternal life."