。
I slid down the muddy slope, slipping and sliding.
Literal
I [topic-は] muddy slope [object-を] slippingly slid-down.
ぬかるんだ ('muddy,' from ぬかるむ 'to become boggy') is the past-as-attributive form modifying 斜面 'slope.' ずるずる is a mimetic for something sliding or dragging slowly and uncontrollably — here perfectly capturing the helpless slipping down a wet hillside. The adverbial と after ずるずる marks it as modifying the verb, same as with other 擬態語.