Despite the seeming urgency of the situation, don't be tricked into acting immediately. The fight doesn't begin until you put the ADAM Harvesting Tool in Fontaine. Take this time to explore the area, and find this Gene-Bank. You'll be able to re-spec your Tonics and Plasmids as you wish.
Find this corpse at the back of the room.
Note the location of this Bot Shutdown Panel, left of Fontaine. You'll be wanting to use it later.
This Health Station is at the far left corner of the room. Hack it now.
Note the four ADAM containers under your Health and EVE bars. You will need to drain all four to defeat Fontaine.
When you are ready to begin the fight, stick Fontaine with the ADAM Harvesting Tool to drain his first ADAM container.
Fontaine is obviously displeased. He frees himself and attacks in the first of three forms, this one Fire. One tactic that I found useful at this early stage is to freeze Fontaine with Winter Blast, then use Telekinesis to throw explosive barrels and canisters at him.
By far the easiest way to defeat Fontaine is to use Electric Gel. Here I am in a previous run. You can defeat Fontaine using nothing but Electric Gel if you have a full load.
Whatever you do, don't let him get this close. His Bouncer-like melee attacks are disorienting, making it difficult to retaliate or even get away.
When his health bar is depleted, Fontaine will return to his ADAM station. He is vulnerable during this limited period of time. Hit him again with the ADAM Harvesting Tool to drain his second ADAM container.
Immediately head left to the Bot-Shutdown Panel and stop the alarm. Hack any bots you can find.
The bots are surprisingly effective against Fontaine, now in Ice form. Winter Blast will not work against him in this form, but Telekinesis-thrown explosives still inflict significant damage.
His health depleted a second time, hit Fontaine with the ADAM Harvesting Tool once more. You can't save your game and there are no Vita-Chambers here, so stay sharp!
Fontaine, now in Electric form, summons an army of Splicers. Enrage! turns them into your allies, keeping Fontaine distracted.
Just don't expect them to inflict as much damage as the hacked Security Bots. I still prefer to toss explosive canisters and barrels with Telekinesis, though the Grenade Launcher is also a fine choice.
Fontaine's health depleted once more, hit him with the ADAM Harvesting Tool for the last time.
The Little Sisters pile on in the subsequent cutscene. Ouch.
One of three possible endings plays. This is my favorite, shown if you have rescued all of the Little Sisters.
Harvest any of the Little Sisters and witness this brutal ending where the world is beset upon by you and your Splicer army. For me, this ending holds the greatest appeal for a sequel. If you harvested all of the Little Sisters you'll see the same ending, but Tenenbaum's narration will be exceptionally damning. And that's it. You have beaten BioShock! I hope you enjoyed the game and I hope this walkthrough helped you! Game on!