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Results found in several dictionaries: Collins, Collaborative Dictionary
shaggy  adj  (shaggier compar) (shaggiest superl )
[hair, beard, mane] 
greñudo 
[fur, eyebrows, animal] 
peludo 
[carpet, rug] 
de mucho pelo 
[person] 
melenudo, greñudo 
shaggy dog story  chiste  m  largo y pesado 

Collaborative Dictionary     English-Spanish
'shaggy' found in translations in Spanish-English dictionary
intonso exp. shaggy Reverso General Dictionary 

"Collins Spanish Dictionary 8th edition published in 2005 © William Collins Sons & Co Ltd 1971, 1988 © HarperCollins Publishers 1992, 1993, 1996, 1997, 2000, 2003, 2005"