Tigra was not Darkseid's first choice as a wife. He originally married Suli. Unfortunatly for Darkseid, Heggra didn't approve of Suli, and hired Desaad to kill her. When the deed was done, Heggra forced her son to marry the woman of her choosing, Tigra.
When Darkseid first went through the Infinity Pits, one of the first things he was going to do was murder his wife. When he was preparing to use his new Omega Beams for the first time, Tigra told her enraged husband that she was with child. Darkseid let her live for this.
Long after Tigra had her son Orion, she claimed he was not Darkseid's son. Tigra stated how she only told him she was pregnant to save her own life, knowing Darkseid wouldn't turn down an heir. In this telling, she says she was never truley pregnant when she told this to Darkseid, so she met with a captian of the Imperial Guard. She says the only thing that mattered was that he was handsome and willing.
A few months later Darkseid had other plans for Tigra. In exchange for slaying Suli, he decided to have Desaad kill his mother, Queen Heggra. He figured having a child during this time wouldn't be appropriate, so he had Tigra imprisoned in a Bio-Freeze Pod until he was ready for his child to come.
It wasn't until almost a thousand years later that Darkseid decided he was ready for Tigra to have her son. Tigra went off and had her son as far away from Darkseid as she could. The lackies who helped her deliver said she never screamed, but hissed, and the baby didn't cry. She killed one of them while giving birth to her son. She named the boy Orion.
During this time, Apokolips was in war with it's neighboring planet, New Genesis. To stop the war, Highfather and Darkseid decided to trade sons. Darkseid gave Highfather Orion for his son soon to be known as Mister Miracle. When the word came to Tigra's ears she came into a rage. To settle her down, Darkseid had Tigra locked up.
Years later, Orion came back to Apokolips. Quite loyal to Highfather, and wanting answers to his life, he tried to find Tigra. It took him six days of rumaging through the planet to find her. Orion broke Tigra out even though she was reluctant to go. She told him that no matter if her body is free, her soul will never be for she has witnesed the gentle nature of Darkseid.
Being jealous of Tigra for being married to Darkseid, Desaad's second in command, Justeen, had Tigra assassinated.