Starting with him stealing the Amulet. He seals up an entrance while being chased by Jabor to buy some time only to find Faquarl there, so he removes the seal and causes Faquarl to get hit by one of Jabor's detonations, and then flies off as a peregrine falcon.
Single-handedly defeating everyone in Pinn's shop in quick succession, including Pinn himself, Simpkin, and two mannequins with djinn inside them that were guarding the shop. Simpkin manages to alert the police and Bartimaeus is captured, but still.
After Lovelace sends Faquarl and Jabor to break Bartimaeus out of prison, Bartimaeus then escapes from them by setting Faquarl on fire.
Jabor chases Bartimaeus and Nathaniel onto the roof, and starts firing detonations at Bartimaeus. Bartimaeus dodges them as best he can, but starts to tire out. He fires a detonation of his own, but it flies far too low to be of any harm to Jabor. Jabor laughs... and then falls through the roof he is standing on, which has been weakened by the detonations fired by both Jabor and Bartimaeus, and into the burning building, which collapses on top of him.
Tricking Jabor into flying into the rift, as well as tricking Lovelace long enough to grab the Summoning Horn.
Also a few things he does in the second book.
Bartimaeus being the only djinni to survive his encounter with the golem.
Summoning a freaking hurricane and sending the Mercenary flying down a hill. It only stops him long enough for Nathaniel and Bartimaeus to escape, but still awesome.
Flying Nathaniel through a building to save him from a group of police in Prague.
Not a particularly flashy or showy one, but awesome nevertheless... Nathaniel makes an agreement with Kitty that she will lead him to the Staff of Gladstone and in return he will let her and her friend Jakob go and offer them safe passage out of the country. He orders Bartimaeus to kill her if she does anything to break their agreement. After she shows him to the staff, he reneges on things and tells her that he'll be taking both her and Jakob to the Tower of London for interrogation. Sure enough, she tries to escape the first chance she gets. Bartimaeus does nothing and Nathaniel is caught quite off-guard. As soon as he gets the chance, he chews Bartimaeus out, threatening him with the Shriveling Fire for not obeying.
Bartimaeus: But that agreement is null and void. You broke it yourself, not two minutes ago–in a particularly noxious manner, if I may say so. So she can hardly be breaking it herself, can she? Listen, if you put that Staff down, you can tear your hair out more easily.
Gets a joint Crowning Moment of Awesome with Nathaniel in the third book when Bartimaeus is summoned into Nathaniel's body to jointly defeat the other spirit-human hybrids running amok. And the moment the aforementioned spoiler happened, he claims to be ten times the djinn he's ever been before! It may say more about how horrible being on Earth is to spirits, but the moment he's protected from it, even severely weakened from what seems to be the spirit equivalent of starving(or possibly suffocating), he's ten times stronger than ever before. Makes you wonder what he'd be capable of it he did it at full strength. And then you realize, we never get to see that. The entire series, every awesome thing Bartimaeus has done throughout the series... is being done on a tiny percentage of his real power.
In spite of being heavilyweakened due to staying in the mortal world for too long, Bartimaeus is still able to keep just ahead of the band of foliots pursuing him and return to Nathaniel... as a frog of all things.
Naturally, he gets a number in the prequel as well.
After making short work of some undead guarding a temple, Bartimaeus collapses the temple on Naabash, the spirit protecting the artifact there.
We finally see Bartimaeus kill one of his masters. May cross into Nightmare Fuel.
Even as he's about to get beaten up and sealed inside a bottle by a freaking marid, he still has time to destroy all of Khaba's collections and reference books as well as set free all the spirits trapped in essence cages!
The entire sequence where he helps Asmira break into Solomon's quarters.
Getting the Ring of Solomon. More or less under Solomon's nose!
Impaling Ammet with a tree.
Using the Ring of Solomon and turning the tables on Ammet. Note that even holding the Ring is greatly damaging to his essence, let alone putting it on and using it.
Finally, returning to the palace in the form of Ammet and punching Khaba into a table.
Nathaniel remembering how to dismiss Ramuthra, saving everyone trapped in the conference hall.
The death of the Mercenary. Nathaniel is trapped between the Mercenary chasing him on one side and the heavily-guarded chamber holding Gladstone's Staff and the Amulet of Samarkand on the other. (The chamber is guarded by a pestilence, which essentially eats away the flesh of anyone exposed to it.) Nathaniel runs into the chamber and grabs the Amulet before the pestilence kills him, protecting him from its further effects. The Mercenary tries to follow. He takes a few steps forward, and the pestilence begins to eat into his clothes... He ends up as a crumpled skeleton on the floor.
Killing Schyler with nothing but a few party gimmicks.
Kitty stopping the Golem.
Also summoning Bartimaeus by herself.
And being the only known human besides Ptolemy to visit the Other Place. The concept was well known enough that Nathaniel - admittedly a protege magician - knew about it, but he considered it an insane idea, and being who is he is, its probably in keeping with the rest of magician society's opinion. Hell, Kitty should probably get another awesome moment for getting the most vital component of the spell: a spirit willing to help her. And Ptolemy for coming up with the idea and being such a great guy to Bartimaeus that he'd be willing to help the first time, and willing to die with him - which he only didn't because Ptolemy sent him back to the Other Place.
Killing a foliot using only her bare hands and resistance to magic.
Jabor gets one when he fights an entire horde of Horlas and Utukku and survives.
Faquarl beating up the Mercenary bare handed.
Also Curb Stompingfour djinn, including Bartimaeus, sent to capture him. Granted, they weren't expecting it; they were really after Mr. Hopkins, whose body Faquarl was residing in. Not to mention Bartimaeus was severely weakened at the time.
Honorius completely destroying the Resistance. While portrayed in a somewhat sympathetic light, it was strangely refreshing to see the Resistance get their butts kicked after touting their resistance to magic among themselves for so long. (They were practicing terrorism after all, and in the end it was really a matter of Gray and Gray Morality.)
The revenge of Jakob's family on Tallow. See Chekhov's Gun on the main page.
Asmira killing the four robbers trying to rob and kidnap her.
Cutting off Khaba's finger, allowing Bartimaeus to grab the Ring of Solomon.
Stuffing her silver charm down Gezeri's mouth, destroying him.
Solomon's speech intended to persuade Asmira not to take his Ring. Doesn't work, but still awesome.
While stupid and completely futile, you have to give credit to Simpkin for sticking with the shop and trying to fight the golem.
Pinn being the only one of the entire cast of sycophant magicians able to fight the Makepeace takeover
Jessica Whitwell defying the demons at the end of Ptolemy's Gate. She refuses to summon a demon into her, and saying she would rather die, summons her Djinni and runs for the door. She is then killed by Nouda, but provides time for Nathaniel and Kitty to get away.