Ivar is definitely one of the most hated characters in smartest of the Sons of Ragnar. From his childhood in constant pain, being constantly fussed over by Aslaug, to his time as King of Kattegat, and eventually to his death on the battlefield, Ivar has a sweeping character arc that takes him from victim to villain and back again.
Throughout that time, Ivar often makes brilliant decisions - especially when it comes to battlefield tactics - but he often lets his rage and insecurity get the better of him. These are the decisions that shaped his life.
Best: Building Himself Crutches & Chariots
Ivar is defined by his physical differences, from the moment of his birth, when Ragnar attempted to leave him out in the cold to die (believing that Ivar would not be able to live a fulfilling life as he was). However, he finds increasingly innovative ways to overcome his inability to walk, from deg custom-made crutches and a leg brace to the chariot that he uses to be able to fight on the battlefield. These prove his creative brilliance, and his refusal to be treated as weak or left behind.
Worst: Attempting To Sleep With Margrethe
This was a terrible decision on multiple levels. Margrethe was enslaved, and three of Ivar's brothers were also sleeping with her - which led Ivar to want to have sex with her as well, as he wanted (at this point) to do everything they did. Margrethe agreed, but when Ivar found himself physically incapable, he was enraged, and threatened to kill her if she told anyone.
This is a terrible decision for those reasons alone, but things became so much worse. It was this event that spurred Ivar on to even greater rage, and that led to him murdering his brother later on.
Best: Going To England With Ragnar
When Ragnar wishes to return to England one final time, he takes Ivar with him. He actually asked all his sons, but the rest refused - however, this journey would prove to be life-changing for Ivar. Not only was he able to find a connection with his father and get his approval, but he was able to meet Alfred and start to learn the principles of battleground 'gameplay' that would stand him in good stead in the future, as the two future enemies played chess together.
Worst: Killing Sigurd
The schism between the Sons of Ragnar had repercussions that lasted for the rest of their lives - and it all started here, at the moment that Ivar killed Sigurd. In many ways, this started long before, when Margreth revealed to the brothers that Ivar wasn't able to perform sexually with her.
When Sigurd teases Ivar about it publicly, he loses his temper and flings an ax at him, killing him in an instant. Not only did he kill his brother, but this launched the eventual war between him and Ubbe, as his older brother saw what Ivar was becoming.
Best: Battle Tactics In York
In York, Ivar managed to take a city that seemed impossible - with the first of many examples of brilliant cunning and the kind of military strategy that would win him so many more battles to come. Hiding in the sewers to trap the men of York, and then leaping out to slaughter them all was the kind of plan that only Ivar - who would later include traps and hidden spikes in his final battle - could come up with.
Worst: Holding A Grudge Against Lagertha
In some ways, it is understandable why Ivar held such a grudge against Lagertha - she did kill Aslaug, who wasn't just his mother, but the woman who had loved him more than anyone else for his whole life. However, where most of his brothers (especially Ubbe) were able to get past her revenge-killing, Ivar never did. This created more division, strife, and war, which was easily preventable.
Best: Heading To Russia
After he was toppled as King of Kattegat, Ivar fled Norway and ended up traveling to Russia, where he met the Rus Vikings - and became embroiled in their power struggles.
This wasn't always a good thing, as the battle between Oleg and Dir for political control was extremely risky. However, here he was able to find a safe haven to recover, a place to launch a new attack on Kattegat from, and somewhere that helped him better understand what living under a tyrant meant, and to grow as a person.
Worst: Declaring Himself A God
When Ivar was ruling Kattegat, for a time it seemed as though he may be accepted, but he grew increasingly tyrannical and power-hungry. His wife, Freydis, encouraged this - telling him to see his inability to walk as the gods having marked him out as special, and eventually convincing him to declare himself as a god. He and Freydis erected a statue to him, and had a ceremony to claim his godhood - something that was the peak of his hubris, and that started to truly turn the people against him.
Best: Becoming A Father Figure To Igor
While with the Rus Vikings, Ivar started to really change, and a lot of that was because he became a protector and father figure to Prince Igor. The young Prince looked up to Ivar, and found in him a friend and ally against his uncle - and the two ended up developing a real and tender relationship. This may have been what Ivar had hoped to have with his son with Freydis, or it may simply have been that it was the first time that he was not seen as the weakest, but as the protector. Whatever it was, this found him a true ally, and a way to become a gentler person.
Worst: Ignoring Hvisterk's Warnings About Blue Eyes
Ivar is referred to throughout the show as a 'cripple', but the reason for his inability to walk and the twisted shape of his legs is never revealed (as the Vikings wouldn't have known what it was). However, it is also shown throughout the show that when the whites of Ivar's eyes are particularly blue, he is at great risk of breaking a bone - and in the final battle, Hvitserk warns him that his eyes are very blue. Despite the warnings not to go to battle that day, Ivar rushes in, eventually onto the field itself, where he dies. It was a fitting end for the character, but a heartbreaking one that may have been prevented if he had listened to his brother's warnings.