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