Many far-fetched things you try to come up with, nature did it first. They already exist macroscopic unicellular algae, although not so big, they are spectacularly big. Just have a look at [these](https://en.wikipedia.org/wiki/Valonia_ventricosa) [two](https://en.wikipedia.org/wiki/Acetabularia).

As you can see from the links, they are very different from each other (in fact, one of them is mononuclear).

### [Valonia Ventricosa](https://en.wikipedia.org/wiki/Valonia_ventricosa)

This would be the easiest approach. Searching for differences between it and other more common, microscopic unicellular beings, I found out that thay are almost identical. So just:

- Make it bigger.
- Multiply the cell components, simply put more of them.

And that would be pretty much it. According to the description in the question, I think **this is the approach you were looking for**. Just a big unicellular [blob](http://tvtropes.org/pmwiki/pmwiki.php/Main/BlobMonster) *(Warning! TV Tropes link)*.

### [Acetabularia](https://en.wikipedia.org/wiki/Acetabularia)

This other approach is more complex. In fact, even if it is unicellular and mononuclear, it behaves more like a plant, with a plant-like stalk and root-like rhizoid. With the difference that it has a very big nucleum in the base.

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Another one thanks to [Nathaniel](https://worldbuilding.stackexchange.com/users/7130/nathaniel):

### [Xenophyophore](https://en.wikipedia.org/wiki/Xenophyophore)

There is this other one which looks more like a sponge. It lives at the sea bottom, just like the other two, but in deeper waters. It feeds like the amoebas. From the wikipedia link:
>These giant protozoans seem to feed in a manner similar to amoebas, enveloping food items with a foot-like structure called a pseudopodium.