Yet another way: Edit > Fill > Choose color but with Preserve Tranparency checked.
I tried that
You tried what?
Your screenshot does not seem to show a Layer Style or a clipping masked Solid Color Layer.
If edge pixels are semi-transparent and you want to change that you could
• Layer > Layer Mask > From Transparency
• apply a Threshold (Image > Adjustments > Threshold) to the Layer Mask
Just out of curiosity: is this going to be printed as black-and-white artwork? If it will, then you may not have sufficient image resolution (educated guess based on your screenshot).
For black-and-white artwork, create a canvas at a minimum of 800ppi (1200ppi preferred) at the required physical size it will be printed at.
For example, A4: 297mmx210mm@1200ppi 9922px by 14032px.
Trouble is, Photoshop doesn't allow us to mix layers with different physical resolutions. Nor can we have a true black-and-white only high resolution layer, because that is not allowed (1bit images do not support layers anyway). A work-around is to work at 800-1200ppi resolution, and use black and white only on the ink layer, while we work with full colour on the fill layers. Later the ink and colour layers are separated (ink @ 800-1200ppi 1bit, colour layer at 300ppi full colour) and brought into InDesign for final compositing.
If your machine can't handle that high resolution smoothly, another option is to bring in a 300ppi version of your ink layer in Photoshop, and work at native 300ppi for your colours. Then later export the 300ppi colour layer, and use the 800-1200ppi ink image when bringing them together in InDesign.
This may sound a bit confusing, but it results in the best quality for comics, and illustrations with bitmap inked artwork with colours (or without colour).
If all of this isn't applicable to your situation, or it sounds too much like a bother, then disregard my post :-)
One more alternative solution to convert your line art to pure black and white:
2) Image-->Mode-->Bitmap. Choose 50% threshold.
Bit long-winded, but gets the job done. Make sure to apply this to your line art file only.