How did Ronan the Accuser become so powerful?

When you say;

The Terrans defeated the Kree

I presume that you are talking about in the comics. The comic continuity is not relevant to the Marvel Cinematic Universe, which takes place in an alternate dimension (Earth-199999). As such, the Kree may be very different in the films from in the comics. We have only seen a couple of instances of Kree in the Marvel Cinematic Universe so far, so we don't have that much information to draw upon, but;

We know that in Guardians of the Galaxy, a truce has been drawn up between the Kree and the Xandarians, which implies that they were at war before. The fact that the Xandarians (who are not immortal, as we see many of them die in Guardians of the Galaxy) have been able to negotiate a truce with the Kree suggest that the Kree are not immortal either.

Also in Guardians of the Galaxy, we see that Ronan is able to hold the Power Gem (one of the six Infinity Stones) for a limited amount of time, before embedding it in his hammer. The fact he has to put it in his hammer implies to me that, like the slave girl that works for The Collector, it would have quickly destroyed him. He is also capable of great feats of strength, throwing Drax around like it's no big deal when they fight in Knowhere. So we can see from this that Ronan, if not neccessarily all Kree, are stronger than they might appear.

Additionally, in the Agents of SHIELD season 2 episode "Who You Really Are", we see Lady Sif (an Asgardian) fight a Kree warrior, and the two of them seem to be fairly well matched in terms of strength and durability. This would imply that it isn't just Ronan the Accuser who is strong, it is all Kree (or at least the ones trained in combat).

In short, the Kree are not immortal, but they are very strong, most likely due to their biology rather than any gained power.

Ronan the Accuser is well, an Accuser. An Accuser is a Kree military or paramilitary rank, borderline Knight Templar, a special forces assassin with the right to be judge jury and executioner. Ronan was fanatically so. Individual Accusers are the strongest most powerful of the Kree.

Add to this the army of Sakaarans, Kree client (read: slave) race, that he commanded, makes Ronan very dangerous. He's a military general who went rogue with entire battalions of soldiers.

Then add to that, that Ronan was connected to Thanos, the Mad Titan, who is almost literally a physical god in the Marvel Universe. Nightmare fuel.

In the comics, Ronan is comparable to Thor or Beta Ray Bill in terms of raw strength.

As a Kree, he is well above average strength. As an Accuser, he wears Accuser armor, which is meant to enhance the wearer's strength and stamina. At the beginning of The Guardians of the Galaxy, Ronan executes a member of the Nova Corps, and the victim's blood mixes with what is likely Odium. As seen in Agents of SHIELD, Kree warriors will inhale/ingest the Odium, which provides them with extreme amounts of inhuman power and rage, before finally killing them. This makes them incredibly overpowered, but it's a short-lived experience. Ronan does the unthinkable by soaking in it, providing him with all the benefits of the Odium, free of problems.