We have no gigantic feat or statement as we hoped. Adam causes big explosions of lightning several times and they are pretty big but that's it. He repeatedly states he's the strongest being on the planet and the others don't even try to counter him (Hawkman agrees they can't defeat him and Fate states early in the movie he's too strong for the whole team) so there's that. The only big thing is implied in the post-credit scene. We have Adam in the ruins of the Kahndaq palace facing a drone sent by Amanda Waller to talk to him. The drone projects a hologram showing Waller who threatens him with death if he ever tries to leave Kahndaq and cause problems again. Adam says no one on Earth can stop him to which Waller responds by saying she can send him a bunch of people who aren't from this planet. Adam then tells her to send them all, destroys the drone and we have Superman, played by Henry Cavill (not joking) landing and saying they need to talk. Nothing is outright stated but Waller doesn't correct Adam when he says nothing on Earth is as strong as him and she openly says she intends to send him people like Superman. So based on this and Johnson's own statements, Adam is very likely comparable to Superman.
For abilities now, Atom Smasher doesn't have anything particular for him outside of Size Manipulation and the superhuman physical abilities that come with it. At one point, he buries Adam with a punch for about a minute or two but Adam frees himself and knocks him out with a punch and later he briefly hurts Sabacc but that's it.
Cyclone only has her aerokinesis, which she can use as pseudo-telekinesis (as shown in the trailers with those pipes) and she briefly conjures a wind shield at one moment. She's noted to have a 167 IQ and is shown to be comfortable with advanced tech, she's also regulary mentionned as being an expert at using nanobots.
Hawkman is a bit meh but still nice. He gets some good hits on both Adam and Sabacc but he gets manhandeled most of the time. His mace can turn into an axe, which he uses against Sabacc, and at one point he uses it to channel Adam's lightning and throw it at him. His mace also seems to emit orange energy. Also, Sabacc impales him with a pipe but he survives and is no worse to wear apparently. He also endures a lot of hits from both Adam and Sabacc and gets up. I know he has stuff in the comics dedicated to him but I don't know the rest.
Sabacc is a lame villain but he has good stuff. Outside of superhuman abilities, fire and fly, he can open a breach to Hell to summon demons by sitting on the old throne of Kahndaq. At one point, he's shown projecting orange energy and lightning against Adam, though he does it after opening the breach. He also has a pretty good regeneration, he heals from Hawkman stabbing him with the blade of his axe (deep enough to lift him up with the weapon within his torso) and later from being impaled with a pipe. However, he dies when Adam literally slices him up.
Adam actually has good stuff. Outside of the obvious (lightning, strength, speed, durability, blessed, flight, longevity), he performs a thunderclap at the beginning of the movie and is shown healing himself by projecting lightning on his wound (a large burn-like scar) with his finger. We're shown in a flashback that he sponthaneously created his first suit out of rage (literally, we have a close look of the suit suddenly being created bit by bit from lightning) and later, he conjures a new one, basically Shazam's suit but with black instead of red, for the final battle. Like I said, he can generate powerful explosions of lightning and vaporize people and objects with lightning. He's also shown being able to direct his lightning bolts where he wants. His weaknesses are that if he says the word Shazam, he will turn back into a human form and eternium, a rare metal with mystical properties that exist only in Kahndaq and with which the crown used by Sabacc to get his powers was crafted. Also, Adam is able to fend off several heavily armed ARGUS agents when he's a simple human without powers.
Now the big part, Doctor Fate:
- Energy Manip and Projection, Forcefield Creation, Flight, Precognition (of possible futures and how people will die), cloth manip and creation (he creates ankhs to trap Adam and Sabacc and later creates chains to hold Sabacc)
- He regulary makes objects appear and disappear with a gesture. At first it looks like invisibility since he does it in his car to make the helmet appear but later he makes some food Atom was holding vanish in the same way. So Summoning and BFR.
- He regulary teleports himself and others with his his Magic. So Teleportation.
- Him and his duplicates can hurt the likes of Adam and Sabacc (though not to an enormous extent) and restrain them with enough strength to make them struggle. He can also sponthaneously create more duplicates in instants.
- He puts Adrianna's cousin to sleep with a gesture so Sleep Manip.
- He projects himself to talk with Adam at one point and clearly says he can put his mind out of his body to appear somewhere else so Astral Projection. In the same scene, he asks Adam to let him interrogate an Intergang thug to know where Adrianna's son has been taken and says he will do that by studying his mind so Mind Manip (we don't see him doing it because Adam killed all the thugs).
- At the beginning of the fight with Adam, he conjures a gigantic illusion of the city they're in but like it was 5000 years ago. The illusion also makes him and Hawkman invisible. So Illusion Manip and Invisibility for himself and others.
- As he fights Sabacc alone, he telepathically communicates with Adam to wake him up and motivate him to retake his powers after having abandonned them (he does that all the while fighting Sabacc and generating dozens of clones). In the same scene, he unlocks Adam's special cell which was maintaining him frozen and does the same with his handcuffs. So Telepathy and Technological Manip.
- He confirms but the final battle that he has been alive for at least 100 years thanks to the helmet so Longevity.
- He has some good durability feats like enduring a shockwave from Adam's explosion, physical strikes and flames from Sabacc physically. It should be noted that while Sabacc kills him "simply" by impaling him, Kent doesn't wear the helmet at the time and again we see him enduring powerful strikes from Sabacc and even being hit by his flames some instants before and he almost immediately gets up after being hit by the fire without any real bruise, he willingly takes off the helmet and lets himself getting killed to prevent a vision where Hawkman dies from happening so it's likely his physical abilities are increase to a big degree when he wears the helmet.
- Notable stuff, after Fate's death, Hawkman takes the helmet (he simply holds it in his arm, he doesn't wear it) and uses it to generate clones of himself to fight Sabacc, stating Fate taught him this trick.