Julius Caesar was a towering figure not only in Roman history but also on the world's stage. For this reason, it is hard to mention all his accomplishments.
First, Caesar was a great military general. He defeated many foes. He is most famous for defeating the Gauls. This is recorded in the BG (Bellum Gallicum). He also was successful on the field in defeating his political rival (Pompey) in a civil war. To give you a sense of Caesar's military prowess, we can compare him to Alexander the Great. Julius Caesar was a veritable military genius.
Second, Caesar was successful politically. He was elected to many positions: pontifex maximus, consul, triune of the plebs, and dictator in perpetuity. All of these offices conferred great prestige upon him. Moreover, his last title (dictator in perpetuity) paved the way for Octavian to become princeps of Rome. Hence, Julius Caesar altered the political structure of Rome.
Third, Caesar was also very generous. I know that some people would not place this as one of his accomplishments, but his generous character made a lasting impression on Rome. Moreover, this was why many people loved him. A quote from Sallust that compares Caesar to Cato says it all.
Their birth, age, and eloquence were nearly on an equality; their greatness of mind similar, as was also their reputation, though attained by different means. Caesar grew eminent by generosity and munificence; Cato by the integrity of his life. Caesar was esteemed for his humanity and benevolence; austereness had given dignity to Cato. Caesar acquired renown by giving, relieving, and pardoning; Cato by bestowing nothing. In Caesar, there was a refuge for the unfortunate; in Cato, destruction for the bad. In Caesar, his easiness of temper was admired; in Cato, his firmness. Caesar, in fine, had applied himself to a life of energy and activity; intent upon the interests of his friends, he was neglectful of his own; he refused nothing to others that was worthy of acceptance, while for himself he desired great power, the command of an army, and a new war in which his talents might be displayed. But Cato’s ambition was that of temperance, discretion, and, above all, of austerity; he did not contend in splendor with the rich, or in faction with the seditious, but with the brave in fortitude, with the modest in simplicity, with the temperate in abstinence, he was more desirous to be, than to appear, virtuous; and thus, the less he courted popularity, the more it pursued him.
This question is broad, because Caesar had so many great accomplishments that were political, literary, and historical. He also made some interesting innovations in military and engineering matters. One of Julius Caesar's major accomplishments was to prevent the invasion of Rome by the tribes of Gaul (sort of modern day France and Germany) during the Gallic Wars. This made him very rich, but it also made Rome richer too. It catapulted Caesar's military career.
However, one of Caesar’s biggest accomplishments was something he did right before he died. He chose young Gaius Octavius as his heir. Why is this such a significant achievement? I consider it an achievement to realize how intelligent, gifted, and ruthless this young man was. Octavius was 17 when his “father” died. He was being raised essentially by Caesar’s sister, so there was some contact. Octavius was a sickly child (possibly due to asthma or maybe whatever ailed Caesar himself), and while they definitely had some contact, it’s not clear how much.
However much contact they had, Octavius made an impression on him. Mark Antony being a disappointment, Caesar chose Octavius as a his heir, and changed the course of history when he adopted him in his will. He saw something in this young man. He knew that he had the intelligence and political cunning to fight his way to the top past the likes of Antony and Brutus and all of Caesar’s other enemies.
He did. It took Octavius/Caesar until 30 BC to do it, when he defeated Antony and Cleopatra. He became Augustus, and the Roman Empire was born. With the birth of the Roman Empire, the civil wars ended. There were no more factions. There was no more dissent (that Augustus did not allow), but there was no more bloodshed either. There was the Pax Romana, and 200 years of peace and Roman expansion. Augustus built libraries, sewers, roads, and other public works. There was an expanded grain dole and a standing army, and no more daggers in the senate, which I guess is the biggest improvement.
Caesar accomplished a lot on his own. He was a remarkable public speaker, and the people loved him. He was famous for luck, and for caring about people. He was definitely a self-made man, and he made himself rich on military exploits, but also on military skill. He was a genius. Perhaps one of his greatest achievements was recognizing the heir to his empire.