People who invoke tachyons need to "keep reading": http://math.ucr.edu/home/baez/physics/ParticleAndNuclear/tachyons.html
The bottom line is that you can't use tachyons to send information faster than the speed of light from one place to another. Doing so would require creating a message encoded some way in a localized tachyon field, and sending it off at superluminal speed toward the intended receiver. But as we have seen you can't have it both ways: localized tachyon disturbances are subluminal and superluminal disturbances are nonlocal.
As for a creature made of such particles, how can you have solid objects or any kind of structure at all when the particles travel faster than light relative to each other? It's not like you can have them in formation traveling fast only from your point of view. Special Relativity still holds.
You can find lectures by Leonard Suskind on youtube, meaning anyone can effectively audit his classes at Stanford, for free. This includes full courses in quantum mechanics and introduction to string theory. In one class he covers what a negative mass-squared term really means (an inverted pendulum energy state) and how they end up propagating waves at normal light-speed anyway.
For your specific points,
- structures could not exist. The particles move faster than light relative to each other.
- they don't really travel faster than light, anyway.
- how would it interact? How indeed. Come back to that below. Communication is in the same boat with detection in the first place.
My only thought would be an energy being trope⚠. A quantum field is the fundamental thing, and "particles" are quantized excitations in the field. There are also "virtual particles" and other non-particle excitations and disturbances. In a tachyonic field, the idea of particles gets weird, and being different from quantum fields we're used to you could handwave some effects that exist as patterns in the field with extended lifetimes that are not giving rise to conventional particles. Few hard SF readers would find it implausible, especially if you explained all that and used it to make an energy being more plausible than normal.
You still have to figure out how to get it to interact with normal matter and electromagnetism. That is a problem with any exotic matter that's not atoms and not electrically charged. You get "dark matter", and a dark matter monster could be here right now and not bother me in the slightest!
The tachyons analyzed in the linked treatment are Bosons. Let's suppose you have a fermion version and your creature is made from that. Fermions affect each other via bosons, which are associated with forces (or more generally, interactions). The exotic material needs to share a charge property with our kind of stuff. E.g. if it was electrically charged, it would interact with atoms via electromagnetic phenomena. It would also release Cherenkov radiation with exponentially increasing energy forever, so that's not good.
Real dark matter candidates and seriously considered un-discovered particles include WIMPs, which interact via the weak force. So plausibility leads you there as the path of least resistance.
There's always gravity. But detecting small objects via gravity would be difficult. Maybe anomalies in gravity measurements lead to the discovery, from other experiments involving measuring gravity over short distances. Maybe the WIMP clouds are attracted to our apparatus being used to probe for large extra dimensions or make a perfect reproducible kilogram standard, and these turn out to be not simple clouds but life.