I have an Illustrator file with two 8.5x11 artboards that I need to save out as a PDF around 300-450KB. Is this possible to do without losing quality? And if it is possible, how would I do this?
I have no idea, because I do not know the content of your file.
But here are some general ideas.
"Quality" is a process, according to your needs. You can have a good quality PDF depending on what is your output and file size needs, but that file could be low quality for other needs.
What is inside
This is the main point. Do you have a lot of things happening inside? the file will be large.
If you have just one black dot inside, the file will be tiny.
If you have a lot of text inside you can leave it as text with the font embeded inside. There is an option to embed just the characters present on the text.
There are a few fonts that do not allow to embed them due copyright issues. For this case use another.
If you have just a vector logo inside or just some simple graphics, leave them as a vector, does not matter if it is big or small, the space will be almost the same.
Here start the tricky part:
If you have some elaborated backgrounds. On a copy of ilustrator (you do not want to overwrite your working file with this one) rasterize all the non text content on one layer and leave it as one 200ppi RGB bitmap. Leave your text untuched as text on another layer.
Then try diferent PDF Settings.
JPG compression and move the slider lets say at 75%.
If the PDF is too large make some calculations and resample your one bitmap to 150ppi 100ppi 75ppi.
This combination of haveing one aond only one low resolution RGB bitmap with the photos and backgrounds, compressed by a JPG algorithm and text with the font embeded is the way to have a small PDF to be viewed on screen.
If you need it to be professionally printed
Forget the small size.