Surviving Mars

The difficulty in getting 100 Martianborn while playing as New Ark doesn't stem from any comfort level or birth rate of your colonists—in point of fact, you'll likely have a population explosion well before Sol 100. Rather the difficulty for this achievement stems from the starting conditions for New Ark: you only get a single rocket, $4,000 M in funding, and 0 Research per Sol. Those combined restrictions can severely limit your ability to even get to the point of having people on Mars, let alone allowing them to start getting reproductive.

Be aware that the Church colonists have a doubled birthrate, so you have some flexibility when choosing your Commander Profile. If you absolutely want to ensure that you'll be getting births, you might want to go Doctor: the lowered comfort requirement for births can make even basic domes filled with apartments comfortable enough for your colonists. However, one of Hydro Engineer, Astrogeologist, or Rocket Scientist might be a better choice: with the first, you don't have to worry about water quite so much; with the second, you should be able to find both anomalies and rare metal to exploit to help bootstrap the colony; with the third, you'll have 2 rockets to ferry cargo back and forth, which might make the early game a bit easier. (For reference, my successful run on this used the Doctor profile; I never felt like I desperately needed a second rocket, but better managing water or having access to more anomalies would have been nice.)

Some of this will be down to luck, so you may wish to restart a couple of times to find a favorable tech order. As research will be very limited early game, you'll want to take both Earth-Mars Initiative and Explorer AI as soon as possible to increase RpS to at least 200. Soil Adaptation will also be important to take early, preferably before you get any people on Mars: the Church has reduced production on Hydroponic Farms, and you will need to have a lot of food to support the colony. Mars Crowdfunding is also a good thing to research early, as the extra $1000 M will come in handy. (You may even wish, if the research for it isn't exorbitant, to invest in Martian Patents once or twice to gain further funds; this is less necessary if your first dome can exploit Rare Metal.)

It might be advantageous to pick a map location which has frequent Meteor Storms: the odd meteor strike leaves behind an anomaly which can be analyzed by an RC Explorer for research. Otherwise, prioritize analyzing Breakthrough anomalies with your explorer: if you are really lucky, you might get Superconducting Computing, which turns excess power into RpS.

You will likely want to invest some of the meager starting cash you have in outsourcing initial research, but you'll only be able to afford about $400 M or so: the rest of your starting cash should likely go into getting extra advanced resources and an RC Explorer on Mars. The default cargo rocket is decently outfitted, especially if you use your RC Transport to extract surface metal. The included prefabs should allow you to start fuel production even if you have yet to discover water, thus allowing you to get your sole rocket back to Earth.

Finally, always remember to DON'T PANIC: the Church members reproduce really fast, so you have some leeway in when you first get them to Mars; you might consider spending a rather long time on planet before getting your first set of colonists over; if you need the extra resources, don't be afraid to spend 30 Sols without humans. You also shouldn't need too many passenger rockets: with Doctor I shipped in just 3 or 4 sets of 12 people; my first Martianborn happened within 2 Sols of humans landing, and the initial group had a birthrate thereafter of about 1 per Sol. (Eventually, your Martianborn will grow up and start having children, and then things start to get exponential.) So, good luck, and kifflom brother brother.