We know of about twelve Apologists in the second century, but out of this number there are about five whose works have been entirely lost or from which we have only a few passages. The earliest Apologist whose work we possess in its entirety, is Aristides, a philosopher of Athens, whom Eusebius names immediately after Quadratus. Like Quadratus, Aristides is said to have presented his Apology to Hadrian (c. 117-138).
Here is the reference from Eusebius, Hist. Eccl. 4.3.3.
Aristides also, a believer earnestly devoted to our religion, left, like Quadratus, an apology for the faith, addressed to Hadrian. His work, too, has been preserved even to the present day by a great many persons.
Here is the reference from Jerome, Illustrious Men 20.
Aristides, a most eloquent Athenian philosopher, and a disciple of Christ while yet retaining his philosopher's garb, presented a work to Hadrian at the same time that Quadratus presented his. The work contained a systematic statement of our doctrine, that is, an Apology for the Christians, which is still extant and is regarded by philologians as a monument to his genius.
Robert M. Grant comments on the attestation to Aristides (The Anchor Bible Dictionary, vol. 1, p. 382):
According to Eusebius, both Quadratus and Aristides presented Christian apologies to the Emperor Hadrian at Athens, probably in 124 C.E. Aristides was unknown to scholars for many years, though his work survived in at least two 4th-century papyri (POxy. 15:1778). The Mechitarists of Venice published an Armenian fragment in 1878, and in 1889 J. R. Harris discovered the whole apology in a 7th-century Syriac manuscript at St. Catherine's on Sinai. J. A. Robinson immediately found that the Greek apology had been used for a lengthy section of the Greek novel Barlaam and Josaphat, ascribed to John of Damascus. The text can be reconstructed from the last two witnesses and confirmed by the fragmentary papyri.
On the contents, Grant writes (op. cit., p. 382):
The arrangement is simple: The work begins with a semiphilosophical description of God and then shows that the gods of various nations fall short. These are the Chaldaeans, who worship the elements/planets; the Greeks, who worship human beings, vulnerable and erratic; and the Egyptians, who worship animals. the Jews are better than any of these people but worship angels and observe the ritual law. Christians are best, for they trace their genealogy back to Jesus the Christ and practice pure love and benevolence. The Syriac version emphasizes their dislike of homosexuality, perhaps more appropriately mentioned to Antoninus [to which the Syriac version is addressed] than to Hadrian. Christians are slandered by the Greeks but they are just and holy.
The Apology of Aristides, mentioned by Eusebius, St. Jerome, and other ancient writers and said to have been the inspiration for the great works of St. Justin Martyr, was considered lost until the late nineteenth century, when an Armenian fragment was discovered. Then in 1889 the full text in Syriac translation was found in the library of St. Catherine's in the Sinai. Ironically, it was then realized that the work had never been lost at all: a slightly shortened version of it had been preserved in the well-known Life of Barlaam and Joasaph of India, attributed to St. John of Damascus. The author decided to insert the Apology of Aristides as a sort of rough equivalent of whatever Barlaam actually preached to the Brahmins.)
The aim of the Apology is to show that Christians only have the true conception of God. Having affirmed that God is "the selfsame being who first established and now controls the universe", Aristides points out the errors of the Chaldeans, Greeks, Egyptians, and Jews concerning the Deity, gives a brief summary of Christian belief, and emphasizes the righteousness of Christian life in contrast with the corrupt practices of paganism. The tone throughout is elevated and calm, and the reasonableness of Christianity is shown rather by an appeal to facts than by subtle argumentation.
St. Aristides delivered the Apology around the year 125, when Hadrian visited Athens. His memory is kept by the Orthodox Church on September 12.