After I finished Betrayer of Worlds I did some digging around in the Ringworld sequels and tried to come up with a definitive answer. This is what I came up with.
By Earth date 2780, at the end of Betrayer of Worlds, Achilles is the Hindmost of the Concordance. The second Ringworld expedition takes place in 2878, 98 years later.
In Ringworld Engineers, "Hindmost" says:
"I served my species well, and four Hindmosts served well before me, before the Conservative faction found power to replace my faction."
He claims to be the fifth on a series of five Experimentalist Hindmosts. In Fleet of Worlds, we witness the raise of the Experimentalists to power, under the rule of Nike. After Nike, Baedeker and Achilles followed him according to Betrayer of Worlds. If we are to follow the word of "Hindmost", he is neither. Someone else replaced Achilles, and then "Hindmost" replaced that someone, and then he was deposed.
When Louis asked him why he was deposed, "Hindmost" answered:
"Some of my decisions were not popular. I meddled with human and kzinti destiny. Somehow you learned our secret, how we had tampered with the Fertility Laws on Earth in an attempt to breed lucky humans, and with the course of the First War With Men, to produce reasonable kzinti."
Fleet of Worlds tells us that the meddling with the Fertility Laws was authorized by Nike in 2650. "Hindmost" seems to imply that this was his decision. If that is true, it means "Hindmost" is Nike.
But "Hindmost" continues:
"You know that I agreed to take Nessus as mate if he returned from the Ringworld. He demanded this concession. And he returned, and we mated. Then we did it again, for love. Nessus was mad, and the Hindmost has often been mad, and ... they deposed me."
Nessus had been infatuated with Nike and then with Baedeker, so this seems to imply that either one of these is "Hindmost".
When Louis asked when the superconductor plague was spread, "Hindmost" answered:
"Eleven hundred and forty years ago by Earth time. The Conservatives ruled for six hundred years. Then the threat of the kzinti put Experimentalists back in power. When the time seemed opportune, I sent Nessus and his team to the Ringworld. If the structure had survived for eleven hundred years after the fall of the culture that kept it in repair, it would have been worth investigating. I could have sent a trade and rescue team. Unfortunately --"
This seems to imply that the Experimentalists ruled since 2335 until the time of the first expedition. Which we know is not true, because Fleet of Worlds shows a Conservative Hindmost in power in 2650.
I have now read everything Niven has written so far in Known Space and I can't draw a definitive conclusion about this. I guess we'll have to chalk it up to "Hindmost" lying and to:
Known Space should be seen as a possible future history told by people that may or may not have all their facts right.
Personally, I think "Hindmost" is either Achilles, thean unnamed Hindmost in the series of four he says that served before him, or not a Hindmost at all. I don't think that either Baedeker or Nike are insane enough to act like "Hindmost", and Achilles is known to be incredibly insane.