How can I repair a broken handle on a hole hawg?

The handles appear to be available on ebay for $12.99 stateside. (e.g. https://www.ebay.com/i/182289228254 )

Failing that, depending on what it is made of and how it’s broken you could:

• Glue it - some types of hard plastic can be “welded” with acetone or “hard plastic glue”, or you could use an epoxy. If the glue doesn’t “melt” the plastic then it’s unlikely to last unless your choice of glue and surface preparation is perfect.
  
• replace it (or the broken part of it) with something fabricated from materials at hand.
  
• 3D print a replacement, or have one 3D printed for you - use the broken one as a pattern and design a replacement using e.g. TinkerCAD (free, online, you just need a browser) then if you have no 3D printer, check out the various 3D design sharing sites (e.g. Thingiverse) which all carry integrated 3rd-party printing services.
  

Personally, I’d 3D print one - with careful design and suitable orientation on the printer, even humble PLA, which is safe and easy to work with, can produce an item easily strong enough for this. Just don’t leave it in the sun ‘cos the stuff softens around 70ºC.

I would recommend you look if there are any "3d print" makers around where you live. Ask them to help you with modeling the broken part (take it to them so they can take measurements etc.) and then print it for you. I would also recommend you to choose anisoprint continuous fiber 3D printing in your case. It is very tough and reliable stuff.