There are 7 different ocean biomes, which are outlined on the Minecraft wiki page: https://minecraft.gamepedia.com/Biome
I have found several in the seed shown by Dwaggienite (-1618472320). These are by no means the only locations of these biomes, obviously, but after getting this achievement 4 times, I'm fairly confident that they should help you as well.
Obviously if you've gone for any of the other achievements, like the shipwreck, ruin, and buried treasure, you'll have seen a couple of these.
These locations aren't close, but shouldn't take more than 15-20 minutes to run between. Make sure coordinates are turned on in the settings (and cheats are off), and play on Peaceful just for ease.
I also made sure to actually swim down along the floor to make sure it counted. Might want to do circles.
Warm - Go to the shipwreck near the spawn. The masts are sticking up out of the water.
Lukewarm = 192, 63, -303
Lukewarm Deep = 125, 62, -192
Frozen Deep - Pretty much anywhere where there's ice, but I marked mine at -40, 63, 22. Feel free to come back to this one.
Cold = -212, 62, 6
Cold Deep = 329, 62, 398
Warm Deep = 506, 62, 85 (NeM2K notes in the comments that 149, 32, -259 may be a better location.)
Hope this helps!