Can I use Shedinja's "Vessel of Life" Ability to attach it to a Pokemon that already has another Pokemon Tool card attached?

No, you cannot; the rulebook states "each Pokemon can have only 1 Pokemon Tool attached at any time". However, if there's an effect that overrides that rule, such as Genesect GX's "Double Drive" Ability, then you would be able to attach Shedinja to a Pokemon that already has another Pokemon Tool card attached.

Relevant cards