An octopus (문어, muneo) is read almost entirely through its most obvious feature — eight arms doing multiple things simultaneously — which maps onto handling many responsibilities or opportunities at the same time, for better or worse depending on how the dream feels.
Korean business language actually has a specific idiom built on this exact image: 문어발식 확장 ("octopus-leg-style expansion") describes a company or person overextending into too many unrelated ventures at once, usually as a criticism. A dream where the octopus's many arms feel chaotic or overwhelming taps directly into this reading — juggling too much, spread thin rather than genuinely productive.
An octopus successfully managing all its arms at once, calmly and without visible strain, is read more favorably — real multitasking skill paying off, capability rather than overextension.
An octopus grabbing onto you with multiple arms is read as being pulled into several obligations at once, not necessarily against your will, but worth noticing how many different directions you're suddenly being asked to move in simultaneously.