。
She walked slowly so as not to slip.
Literal
She [topic-は] not-slip [so-as-to-ように] slowly walked.
~ないように creates a purposive negative — 'so that one won't X / in order not to X'. Built from negative ~ない + ように ('so that'). すべる ('slip / slide') is the verb of unintended sliding, common in winter-conditions warnings or after a wet floor. ゆっくり is a 擬態語 for slow, leisurely motion; the と after it is the optional adverbial marker that often glues mimetics to verbs. The whole sentence is the kind of careful description you might find in a 'walking on icy sidewalks' advisory.