Mucky and muddy describe having a lot of wet soil or dirt. Water can be said to be muddy, as well as ground and people. Dirty can be any dirt and any degree. If I have a slight amount of dirt on my pants, they would be dirty, but not muddy or mucky. They would have to have a lot of dirt for that. Filthy is used when something is extremely dirty. Filthy always means dirty. Dirty does not always mean filthy. Also muddy and mucky apply to a particular kind of dirty - one the involves mud.

"mucky" = http://dictionary.cambridge.org/dictionary/british/mucky?q=mucky "dirty" = http://dictionary.cambridge.org/dictionary/british/dirty_1?q=dirty "muddy" = http://dictionary.cambridge.org/dictionary/british/muddy_1?q=muddy "filthy" = http://dictionary.cambridge.org/dictionary/british/filthy_1?q=filthy