Perhaps surprisingly, given how difficult an operation an amphibious landing is (particularly against a defended beach), very few examples of outright failure spring to mind. The two I'm coming up with are Gallipoli 1915-16 and Dieppe 1942.

And even then, despite being a failure, Gallipoli isn't quite what you're asking for but I'll mentioning it anyway. At Gallipoli, the British (and Dominions) landed at a couple of points along the peninsula--at what's now known as Anzac Cove and at Cape Helles (but not at Bulair, which had been considered by the Turks to be a highly probable landing place and which consequently drew a lot of attention in preparing defenses). After a successful landing, the British and Anzac forces, partly through their own slowness, failed to make much progress on the peninsula. In the end, they finally withdrew, an act which actually achieved tactical surprise (which was very important as a contested withdrawal would probably have been an outright disaster). Gallipoli was pretty similar to Anzio in that they both bogged down and became quite tenuous at times, the main difference is that Anzio was eventually supported by a breakthrough of the Gustav Line and so there was no withdrawal. At Gallipoli, there was no main front to take indirectly (and then directly) support the beachhead.

Dieppe is altogether more what you're asking about. An allied force of Canadians, Brits, Americans, and French (but mostly Canadians) attacked the port of Dieppe, on the French coast--total forces of about 6,000. It was billed mostly as a raid, destroying port and coast defense installations and the like, but the commanders hoped to occupy Dieppe for a little while. It was a disaster. The Germans were well prepared, and inflicted heavy casualties on the attacking forces. Some 60% of the attacking force was killed, wounded, or captured and even the Royal Navy lost a destroyer. Granted, it was a "raid" (and not exactly well planned at that) and not an amphibious invasion (6,000 troops is hardly enough with which to invade Europe!). Nevertheless, it's the closest example to what you're asking about as the operation lasted less than ten hours and concluded with evacuation. That said, the Allies in Europe learned a lot of lessons about the difficulty of amphibious operations.

Yes, the Soviets tried to do a couple of amphibious operations against the Germans during WW2 and there were a couple of pretty big failures. An example of this would be the battle of Kerch in which Red Army landed on the Kerch peninsular in Crimea but due to a well led German counterattacks got pushed back into the sea around 5 month later. Over 160,000 Soviet soldiers were killed, wounded or captured, many of whom because the Soviet navy wasn't able to evacuate them in time.

So, I'm no expert, but the battle of Marathon seems to fit the bill. To summarize, the Persians landed an army near Marathon via a naval expedition. The Athenians used a clever military strategy to flank the Persians, which then caused them to retreat to their ships. The Wikipedia article on this battle has a bit more detail if you're interested.

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