I know Achilles was born around 1200-1100 BC because he participated in the Trojan War, but I do not know when Hercules was born, nor Theseus for that matter.
Chronologically, it goes Hercules/Heracles, Theseus, and then Achilles in the main mythological accounts.
Achilles is last. Hercules older by far because he's the one who placed child Priam on the throne, and Priam was far older than Achilles in the Iliad. Achilles was essentially the baby of the Greek kings, likely younger even then Priam's son Hector. So Hercules is far, far older than Achilles.
With regards to Theseus, Heracles is still older. Pausanias has this story about them both going to the house of Pittheus. Heracles is a grown man, and Theseus is 7 years old.
[1.27.7] One of the Troezenian legends about Theseus is the following. When Heracles visited Pittheus at Troezen, he laid aside his lion's skin to eat his dinner, and there came in to see him some Troezenian children with Theseus, then about seven years of age. The story goes that when they saw the skin the other children ran away, but Theseus slipped out not much afraid, seized an axe from the servants and straightway attacked the skin in earnest, thinking it to be a lion.
[1.27.8] This is the first Troezenian legend about Theseus. The next is that Aegeus placed boots and a sword under a rock as tokens for the child, and then sailed away to Athens; Theseus, when sixteen years old, pushed the rock away and departed, taking what Aegeus had deposited. There is a representation of this legend on the Acropolis, everything in bronze except the rock.
Later authors equated the Marathonian Bull that Theseus kills with the Cretan Bull of Heracles' seventh labor, again making Heracles' adventures prior to Theseus'.
Of course, Greek mythical figures aren't real (as depicted), so you might find some inconsistencies in accounts, but I think other stories can fit well with the chronology. For example, in Sophocles' Oedipus at Colonus, Oedipus goes to Athens to see King Theseus. Well, Oedipus' kids fought each other in the war of the Epigoni, which was the war right before the Trojan War. If Achilles was a child or even not born yet during the Epigoni, that would also confirm Theseus' seniority over him.
It seems that during the time of the Dorian conquests that the Local Mycenean men were away at Troy and the Dorians combined Cretian & Mycenean myths with their own to give the Dorians a birthright to the land. The return of Odysseus created a dilemma that was resolved with a ridiculous myth about where Odysseus had been and the question of his return. Re-writing history was common in ancient times for political reasons and I suspect Odysseus was a sea people who got beat bad in Egypt and returned in shame to find his homeland conquered. I suspect all Greek history was re-written into myth during this period, that Perseus & Achilles were combined into Hercules, the prefix and suffix combined to make Perchilles... and even more ridiculous changes. The overall purpose of political re-writing was an attempt to hide their involvement with the sea people, their destruction of the world around them and the shame of their ultimate defeat.