This question in effect asks whether bodiless energy can have life and intelligence.
There are two or three contexts in which a question like this is normally asked. One is the perennial human search for information about an afterlife, a spiritual realm, a soul independent of the body.
Another is exobiology and science fiction - one asks whether there could be beings in the universe that are pure energy, or detached from matter as we know it. This version of the question has some overlap with a transhumanist form, in which one is asking about the possible future descendants or creations of the human race, in the era of technology.
As the comments say, in modern physics, energy and matter are rather united. More precisely, everything is made of quantum fields, each of which has a field aspect and a particle aspect, and energy is always a property of those fields. You never have energy existing completely independently of those fields.
You do still have the distinction between boson fields and fermion fields, which is a little like a distinction between "force" and "matter". So the quest for living energy without body, could mean a search for purely bosonic life.
But before we go there, maybe I should say something about the classic idea of states of matter. There is a classic division of the world - the part of the world made of atoms - into solid, liquid, gas. Then there's also plasma, a gas of ions (atoms which have lost some electrons) and free electrons.
Then if we get into quantum mechanics, there are potentially many more states or "phases" of matter: vacuum condensates, bose condensates, the quark-gluon plasma, ultradense states like those found in a neutron star or a black hole. Even ordinary atomic matter has many states which don't quite fit the classic taxonomy - conductor, insulator, superconductor, anyons, and many more.
So "matter" or "quantum fields" can do all sorts of things, and it would be hard even for an expert to keep track of all the possibilities.
Since this question is about the possibility of a different form of life and intelligence, one interpretation is to say, can life and intelligence exist in any phase of matter, that is completely different to the one that we know about - room-temperature atomic matter, in the solid/liquid form we know as cellular-based life?
The question is vague, the criteria are vague, and the spectrum of possibilities is far from understood. But it is plausible that you need structures that are persistent, but which can be rearranged.
In ordinary matter, this role is played by atoms and molecules.
In some other phase of matter, this role might be played by topological objects, like topological defects - field vortices, "strings", and so on.
I don't know whether this is bodiless enough for the questioner. If you have a spatially extended object, built out of a spatial arrangement of repeated structural elements, isn't that a kind of body, even if it isn't made of atoms? An atom, technically, is just a bound state of charged quantum fields, and these alternative structural elements will also be some kind of bound state of quantum fields.
But that aside, suppose we ask, is there anything in the universe other than atoms which can make complex dynamic structures that exhibit life and intelligence?
Clearly we don't know any such thing. One could imagine large self-organizing structures in plasma, but so far that's just a science-fiction concept (ball-lightning lifeforms living in the atmospheres of stars, and so on).
There is the possibility that dark matter contains atomlike entities. According to standard conceptions, the bulk of the dark matter must consist of large halos surrounding and outweighing the visible galaxies, made of particles that hardly interact with each other; but there is room for a fraction of the dark matter to be self-interacting and possibly having its own "dark chemistry" and hence "dark biology". Alternatively, dark matter that is in an extended quantum state, like a superfluid, may contain topological defects, and perhaps something could be made of those. Again, whether either of these would satisfy the questioner is debatable.
I promised to say something about the prospect of purely bosonic life. One might imagine that nonlinear bosonic fields could support solitons and other extended topological structures. The problem here is that the bosonic fields we know about, like gluons, interact with fermionic fields, and so you don't get purely bosonic entities, e.g. glueballs should swiftly decay into hadrons with a fermionic component. One could speculate about geons, the hypothetical gravitational solitons, being a purely bosonic sector that is exempt from this consideration, but there's no mathematical demonstration that such a thing can work.
A quite different direction to take such speculations would be to focus on "information". If we look at proto-spiritual speculation in the hard sciences these days, it is arguably far more often couched in terms of "information" rather than "energy". "Energy" is something of a 20th-century way to think in this domain, inspired e.g. by the reality of the invisible part of the electromagnetic spectrum.
But today we have the idea of computation, and the mind as a computer program, and so the avant-garde way to look for invisible realms of existence is in information and computation. Here one may look for life that exists in an alternative basis of our Hilbert space (was this a David Deutsch idea?), or one may suppose that our universe is a mathematical entity, or is a computer program that exists ideally (rather than a program that exists materially, as something within a material computer).
In an already rambling response, this truly takes us off-topic, but I thought I should at least mention that today's frontier of incoherent science-inspired speculation about other realms of existence is more likely to involve the concept of information rather than the concept of energy.