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With vinegar
Vinegar is highly acidic, and as such, kills plants quickly and effectively.
Fill a spray bottle with vinegar and spray the ivy thoroughly. Be careful to only spray the ivy, as it will kill any nearby plants. After a couple of days, the leaves should turn brown. You can then remove the leaves to minimize any chance of propagation.
If there are still some green leaves, spray those too and repeat the process. Removing leaves that are still alive can damage tree bark and do more harm than good.
