If the cyst is actually a nematode, you need to start by freezing thawing and grinding the tissue to homogenize before you use the kit. Five cycles of freezing in the -80C freezer and thawing should be enough. Good luck!
you probably have lots of protein contamination so you should use a DNA clean up kit. If you have fragmented DNA perhaps you need to look at how fresh the samples are, are they snap frozen? how long are they stored for? is it possible to process fresher? Also do you use the best lyssi method, are you pestle and mortaring or using a homogeniser with RLT buffer?