Unless your printer is postscript or you are using rip software, your only option to be able to print Halftone separations, is to use Photoshop and convert each channel to bitmap mode. This process will create you're halftone dots right into the image itself that you will see on your computer screen. Here is the step-by-step process to follow. CAUTION: DO THIS ON A COPY OF YOUR ORIGINAL
1) If your image in Photoshop is not already in CMYK color mode, convert it now.

2) In Photoshop, make sure your channels pallet is visible. Now we need to convert the color mode to Multichannel.

3) Now in your channels pallet, right click on the cyan channel and select duplicate

This will open another dialog box asking where to save this duplicate. Select the option new document. Make sure the name is cyan

This will open a new Photoshop document with that new cyan channel you just duplicated

4) . Now it's time to create the halftone dots right in the image itself. To do this, we need to convert the cyan channel to bitmap color mode.

This will open up your bitmap mode options. In the drop down menu select Halftone screen then click ok.

This opens another options window
As a side note, in that dialog window, 300 pixels per inch has nothing to do with the halftone sizes or anything else other than just the file's resolution

This step is perhaps the most crucial! There is a formula for this which generally must be followed, otherwise the resulting screenprint Will likely contain crazy morei patterns. It is the screen mesh that is going to be used for the screenprinting which dictates the dot size to use on your films. Simply put, take the screen mesh value and divide that by 5 (I prefer 4.73) Let's assume the screen mesh will be 305 (which is standard for four color process printing) so.. 305 divided by 5 = 61 <--- that value is known as "LPI" (Lines Per Inch)
After 28 years in screenprinting, I'm going to share with you one of the most important secrets that most "separators" are not aware of or do not follow.. Always use the same screen angles for each color!! 22.5 degrees is what I use. If you never ever take advice from anyone, take a leap of faith and take my advice on that! If anyone has questions about that statement, I will be more than happy to explain in further detail.
5) Now that your image has your Halftone dots, we need to convert the color mode to grayscale then convert again to Multichannel


6) Now in your channels pallet, double click that channel which should say Black, and rename it to Cyan and enter the value zero in the solidity option then click on the little black Color Square. This will open another dialogue for you to change the color to process cyan. Click on Color Libraries then select the color swatch Process Cyan then click OK then click OK again



7) Now go back to your original file and right click on the magenta channel and follow the exact same process. Then repeat the whole process for the yellow channel and the black channel.
8) Finally, there will be five documents open in Photoshop. The original, untitled 1 (cyan), untitled 2 (magenta) and so on.. Let's use untitled 1 document as the file we will copy the other channels to. So go to untitled 2 (magenta) document and right click on that process magenta Channel and duplicate it to the untitled 1 (cyan) document. Repeat this process for the remaining two documents.
9) Now your original untitled 1 document should contain all four of your channels. The image will look a bit funky on your screen but if you zoom out making the images look smaller, it will look a bit better.

10) Next go to menu File/Save As.. And select format option "Photoshop DCS 2.0" and make sure spot colors is selected

Select option single file with color composite

11) Now it's time for illustrator. Create a new illustrator file in CMYK mode and setting your art board size to the size of your transparencies you will be printing. Once that new document is open, go to menu "File/Place" and select that EPS file you just made in Photoshop

The Image you just placed into illustrator is going to look funky but don't worry about what you are seeing on the screen at this point. Now if you go to print your separations, you will see your four color channels to print. Don't worry about screen angles or line frequencies because we Already set those up in Photoshop and as far as illustrator is concerned, it's not printing halftone. It's just printing normal spot colors separations.

You could just bypass the whole illustrator process and print the separations directly from Photoshop