The connecting record
statedA Clash of Kings
Cersei Lannister killed Robert Baratheon in A Clash of Kings.
A boar opened him and everyone says so. The wine was strongwine, fortified past what he was used to, and Lancel Lannister carried the skin all day at her arrangement — a thing Cersei lets slip to Tyrion in A Clash of Kings, and that Lancel confesses outright to Jaime in A Feast for Crows, calling the pair of them both kingslayers.
What each of them is ranked on
The killer · Cersei Lannister · off the scale
Never lifts a weapon and never has to. What she does instead is place other men's hands where she needs them — Ser Osney to smother a High Septon, Ser Ilyn Payne seated in the Queen's Ballroom through the Blackwater with orders to cut her own throat and Sansa Stark's if the walls give way. On screen she buries the whole Faith under wildfire from a window across the city. Then the Faith takes her guards away, and what is left is a woman shaved bald and walked barefoot the length of her own capital. That is not a fight she lost. It is the weight of her sort of power once somebody handles it directly.
shownA Clash of Kings · ch. 60 (Sansa VI)
Seats Ser Ilyn Payne, the King's Justice, in the Queen's Ballroom for the duration of the Battle of the Blackwater.
statedA Clash of Kings · ch. 60 (Sansa VI)
Tells Sansa that Payne is there for the two of them, because she will not let Stannis take them alive.
shownA Feast for Crows · ch. 43 (Cersei X)
Has Ser Osney Kettleblack murder the High Septon, and beds him as the reward.
All 5 citations
shownA Dance with Dragons · ch. 65 (Cersei II)
Shaved of every hair and stripped, she walks barefoot from the Great Sept to the Red Keep through a jeering crowd, and breaks down before she reaches the gate.
shownGame of Thrones · S06E10 “The Winds of Winter”
Destroys the Great Sept of Baelor and everyone inside it with wildfire laid beneath the building, watching from a window across the city.
The victim · Robert Baratheon · rank 15
the Demon of the Trident
Rode for Summerhall the hour he heard of the plot, with every knight and squire he had, and beat three loyalist hosts to the rendezvous — three battles in a single day, each lord taken in turn as he came up and before he could join the others — and killed Lord Fell face to face in the middle of it. Came out of a brothel at Stoney Sept when the bells started and left six men in the street, one of them Rhaegar Targaryen's own former squire. Met Rhaegar at a ford of the Trident with the warhammer and drove the ruby dragon on the man's breastplate into the chest behind it, and the stones went into the water and gave the crossing its name. Not one of those sentences is depicted. Each arrives as somebody's recollection — Eddard Stark's, an outlaw's, a maester's — because by the time a reader reaches him he is eight stone over, drinking before the jousting starts, and sending two Lannister squires off to borrow a breastplate stretcher that does not exist. He is the plainest demonstration here of what ranking a fighter at his best costs a page: the largest hour in the tier, and nobody ever watches a minute of it.
statedA Storm of Swords · ch. 54 (Davos V)
Warned by an informer, he rode at once with all his knights and squires, reached Summerhall ahead of the loyalist lords, and beat the hosts of Cafferen, Fell and Grandison in three battles in one day before they could join up, killing Lord Fell in single combat.
statedA Dance with Dragons · ch. 9 (Davos I)
Slew Marq Grafton at the taking of Gulltown at the start of the rebellion.
statedA Storm of Swords · ch. 29 (Arya V)
Harwin tells Arya that when the bells rang at Stoney Sept, Robert came out of hiding and "slew six men that day, they say", Ser Myles Mooton among them — hearsay, and marked as such by the teller.
All 15 citations
statedA Dance with Dragons · ch. 61 (The Griffin Reborn)
Jon Connington remembers being very nearly killed by him on the steps of the town's sept that day.
statedA Game of Thrones · ch. 19 (Jon III)
The spiked warhammer was forged for him at Storm's End by Donal Noye.
statedA Game of Thrones · ch. 4 (Eddard I)
Eddard remembers the two of them circling in the shallows until a crushing blow of the hammer stove in the ruby dragon and the chest beneath, and men of both armies scrabbling for the stones afterwards.
statedA Storm of Swords · ch. 21 (Jaime III)
Jaime Lannister reckons him the stronger of the two of them.
statedA Feast for Crows · ch. 24 (Cersei V)
Preferred the melee to the lists, where he could hit men with a blunted axe or hammer.
statedA Game of Thrones · ch. 4 (Eddard I)
Six and a half feet tall by Eddard's reckoning, and grown at least eight stone in the nine years since Greyjoy's Rebellion.
shownA Game of Thrones · ch. 30 (Eddard VII)
Too fat for his own armour at the Hand's tourney, he sends Lancel and Tyrek Lannister to Ser Aron Santagar for a breastplate stretcher, and Eddard and Barristan Selmy argue him out of the melee.
statedA Game of Thrones · ch. 30 (Eddard VII)
Varys tells Eddard afterwards that the queen had arranged for the king to die in that melee.
shownA Game of Thrones · ch. 47 (Eddard XIII)
Brought back to the Red Keep gored open by the boar, he dictates the will and asks for the order on Daenerys Targaryen to be called off.
statedA Game of Thrones · ch. 58 (Eddard XV)
Varys points out that Lancel Lannister kept the king's wineskin full for the whole of the hunt.
shownGame of Thrones · S01E05 “The Wolf and the Lion”
Set on riding in the joust, he torments Lancel Lannister over the armour that will not close and sends him off on an invented errand, and Eddard Stark tells him he is too fat for it and that no knight would dare unhorse him.
statedGame of Thrones · S01E07 “You Win or You Die”
Barristan Selmy says the king made everyone stand aside so that he could take the boar by himself.
What this does not settle
One death in one work. It is the only place the record puts these two in the same room, and it is evidence about that meeting and nothing wider — not a general matchup, not a rematch, and not a ranking of its own.
The ladder above it is argued from everything either of them has been shown doing; this page is argued from one citation.
Where the two disagree, the disagreement is the point, and it stays visible rather than being resolved by whichever of them happens to be on this page.