Demigods are special humans that are born partly divine. These invidividuals have been extremely rare throughout history, and always have various significant effects for the world around them, leading to important changes for their time period. Demigods are marked by their exceptional beaury, amber colored eyes and golden blood, symbolizing their divine status. They are also human characteristics amplified, and are far stronger, faster, and more intelligent than average.

However, there are a number of problems relating to their development. A demigod coming into existence is very risky for a human mother to carry to term. During their fetal stages, they require significantly more resources from the mother, and grow at a quicker pace. In addition to that, a mother carrying a god-like fetus would likely suffer serious injury when the fetus begins to kick. All of these conditions would likely kill her.

How can a mortal woman successfully carry a demigod to term?

The demigod baby shares the blood supply with the mother, during this time, she also shares the divinity, the strength, and the partial invulnerability. Think "Mirror syndrome" but in a positive way. Instead of a shared illness, it's a shared invulnerability.

Fat mothers.

Fat provides nurishment as well absorbtion of shocks. Having a fat if not obese mother seems to be the most likely way to guarantee survival, even if the mother will be battered and bruised. This could easily expedite the demigod's status as in antiquity only rich and powerful people would get enough food to get fat. So expect the best teachings and equipment available.

If your demigod foetuses come to term faster, requiring more resources in order to grow at a quicker pace, that may (in some way) be helpful for the mother. Rather than having to endure nine months of internal bruising, if the foetal development is complete in, say, three months, then perhaps she won’t need to deal with prolonged pain.

Also, in order to provide for a fast-growing foetus, it might be preferable for your mother to have ready access to as much food and drink as she requires (i.e. she’ll probably have to be quite wealthy, if this is a historical setting).

Also, the other thing to remember about demigods is that they are half-human. While they may benefit from accelerated healing, growth, intellect, and so on, it might be that during pregnancy, they simply act the same as a normal human foetus, just in a shorter timeline. Once they’re born, and exposed to the outside world, that’s when their godlike powers begin to kick in.

It also make sense that the gods who impregnated these women in the first place actually have a vested interest in their offspring. If they don’t care about their child (or the mother), they’ll do nothing to aid the process. However, if they do want to ensure the safety and survival of their child (and also the mother), then cue some divine intervention. They could perhaps imbue the mother with a secondary womb-lining/placenta, one that acts both as a shock absorber, and feeds the foetus the godlike nutrients they need.

Another idea is that maybe the mother has to ingest god-food (nectar and ambrosia) - ordinarily a human couldn’t tolerate it, but given the nutrient needs of her foetus, and the non-human behaviour it exhibits while she’s carrying it, it serves to strengthen her enough (and provide the baby with the divine nutrients it needs).

Same as for normal living beings.

Natural selection: only demigods who manage to not kill their mother in their fetal stage get the chance to be born and pass their genes to their descendants.

All others are simply subject to Darwinian selection.

If you want to sprinkle some divine intervention in the picture, than the deity who impregnated the woman will also put some abracadabra to ensure she can bear the fetus until a suitable age.

Do not make a problem where you do not have one

Demi-gods have been born by fully human mothers in hundreds of myths all around the world for thousands of years without anyone ever making an issue out of it, so you do not need to make an issue of it now.

In fact if you do make an issue of, you are more likely to hurt your work than help it. This is because the corollary of Chekhov's Gun applies here: if you do not intend to have this "issue" be important to the story, do not make it part of the story. You do not need to explain it unless it is relevant to the narrative.

"But..."

No, you do not really want to go there because of the immense amounts of squick this implies.

Human beings have neither the aural nor the psychological capacity to withstand the awesome power of God's true voice. Were you to hear it, your mind would cave in and your heart would explode within your chest; we went through five Adams before we figured that one out. — Alan Rickman as Metatron in Dogma

So let the audience assume that it just worked out, as they have done for — quite literally — thousands of years without anyone raising as much as an eyebrow about it.

On the contrary, the human mothers of part- or fully divine figures seem to be able to conceive, carry to term, and then give birth in remarkably carefree ways...

"Now the birth of Jesus Christ was in this wise. When his mother, Mary, was espoused to Joseph, before they came together she was found with child of the Holy Ghost."

Yes, and the Greek demigod Perseus was born when the god Jupiter visited the virgin Danaë as a shower of gold and got her with child. The god Buddha was born through an opening in his mother's flank. Catlicus the serpent-skirted caught a little ball of feathers from the sky and hid it in her bosom, and the Aztec god Huitzilopochtli was thus conceived. The virgin Nana took a pomegranate from the tree watered by the blood of the slain Agdestris, and laid it in her bosom, and gave birth to the god Attis. The virgin daughter of a Mongol king awoke one night and found herself bathed in a great light, which caused her to give birth to Genghis Khan. Krishna was born of the virgin Devaka. Horus was born of the virgin Isis. Mercury was born of the virgin Maia. Romulus was born of the virgin Rhea Sylvia. For some reason, many religions force themselves to think of the birth canal as a one-way street[.]

Christopher Hitchens — God Is Not Great

A demigod's powers only manifest after birth

While in the womb, the demigod is, for all practical purposes, a normal human child. This requires no additional resources and incurs no additional risk upon the mother. This also creates a brief time of vulnerability in which the demigod can more easily be killed: either by killing it in the womb (usually killing the mother as well) or very soon after birth, before the child's abilities become more than human.

This has been discussed in detail in the modern mythological framework here: https://en.wikipedia.org/wiki/Man_of_Steel,_Woman_of_Kleenex
In Niven's analysis: No, Lois Lane can not safely carry Superman's child to term. In fact problems arise almost immediately.