Antimony, beryllium, chromium, cobalt (Co), gallium (Ga), germanium, indium (In), lithium, niobium, tantalum, the platinoids, the rare-earth elements (including dysprosium, Dy), and tungsten are generally regarded to be critical (rare) metals, and the ions of some of these metals are stabilized in acidic solutions. We examined the adsorption capacities of three water-soluble functional polymers, namely archaeal poly-γ-glutamate (L-PGA), polyacrylate (PAC), and polyvinyl alcohol (PVA), for six valuable metal ions (Co(2+), Ni(2+), Mn(2+), Ga(3+), In(3+), and Dy(3+)). All three polymers showed apparently little or no capacity for divalent cations, whereas L-PGA and PAC showed the potential to adsorb trivalent cations, implying the beneficial valence-dependent selectivity of anionic polyelectrolytes with multiple carboxylates for metal ions. PVA did not adsorb metal ions, indicating that the crucial role played by carboxyl groups in the adsorption of crucial metal ions cannot be replaced by hydroxyl groups under the conditions. In addition, equilibrium studies using the non-ideal competitive adsorption model indicated that the potential for L-PGA to be used for the removal (or collection) of water-soluble critical metal ions (e.g., Ga(3+), In(3+), and Dy(3+)) was far superior to that of any other industrially-versatile PAC materials.