Handwaving away some of the problems here, one basic one appears insurmountable: Decoherence. This is a process that involves the destruction of the superposition of a quantum system. The loss of quantum coherence is a major experimental problem in, among other things, quantum computing. Minute interactions with the outside environment - heat, light, vibrations - can all destroy the superposition of the qubits. In quantum computers, decoherence happens on timescales of tens of minutes even in a best-case scenario.
Quantum computers can use error-correction codes and high magnetic fields, among other things, to account for and mitigate this decoherence. However, your creature will presumably be living in the natural world, not in a laboratory - and there are plenty of sources of perturbations to cause decoherence. This means your creature likely will be unable to maintain this superposition for any significant amount of time.
The obvious general solution is to isolate the creature from its environment as much as possible. That would ideally involve placing it in an area of near-pure vacuum, surrounded by high magnetic fields and maintained at extremely low temperatures. Regions of outer space seem the natural best spots, outside a high-tech laboratory. Some sort of biological magnetic field could deflect charged particles, and a low density of ambient neutral particles could ensure that the creature stays in a superposition for a longer time. Life in space is tricky, but not impossible.
Unfortunately, an Earth-like environment will lead to decoherence very quickly.
Let's say we handwave that away. We still need a way for the creature to choose which specific state to collapse to. That means it needs to change its wavefunction. In all likelihood, the initial wavefunction is a mixture of a bunch of (let's say linearly independent) states. Assuming that each state is equally likely for the creature to end up in, its wavefunction looks something roughly like
$$|\psi\rangle=\frac{1}{\sqrt{N}}|1\rangle+\frac{1}{\sqrt{N}}|2\rangle+\cdots+\frac{1}{\sqrt{N}}|N\rangle$$
where each $|n\rangle$ is a particular state; the particular numbers are just to differentiate them from each other. The factor of $\frac{1}{\sqrt{N}}$ indicates that there is a probability of $\frac{1}{N}$ that the creature will end up in a given state. To make it more likely that the wavefunction will collapse into a particular state, the coefficient of a particular basis state will need to be changed. If the wavefunction can be manipulated somehow, it could be more likely that the creature ends of in a desired state.
At the end of the day, however, quantum mechanics is fundamentally probabilistic. Even if quantum mechanical effects influence this creature, you can't guarantee that it will end up in the state you want - and that might be problematic.