It's unclear if your issue is the text being blurry or the images. But let's assume your images have the right resolution and were not resized bigger, or didn't lose any quality in that way.
If the texts are blurry, you can cheat and convert your PSD layer file to PDF, and still keep the sharpness of a vector.
From the screenshot that is still visible, it looks like a question of text trapping in Photoshop. You can fix this in 2 ways:
1) Convert that Photoshop text to vector
Simply save your file in .psd with the layers, and open that file in Illustrator. Choose the "convert layers to objects" and your text layers from Photoshop will be transformed into vectors.
Now export that PDF with the highest quality setting or no compression at all, and open it again the way you took your screenshots to see if the issue still happens.
If you're satisfied, you can follow these instruction to optimize your PDF to be a smaller file size but retain the same print quality:
"Adobe PDF file too big, what are my options?"
2) Add some trapping in Photoshop
If you don't own a license of Illustrator or simply don't want to use it, you could try to add some pixels to your trapping on your text in Photoshop. This will hide the anti-aliasing you might see on the final result but it will not improve the quality of your file
To do this, go on the menu "image" and select "trap". In this box, add 1 or 2 pixels of trapping. Usually 2 gives good results.
Don't forget to keep another version of your Photoshop with layers; trapping like this will require your to flatten your file and you also need to be in CMYK color mode!