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A Peaceful challenge is a challenge run in which the goal is to complete a section of GT:NH while remaining in peaceful mode. This can also include some extra rules such as not attacking some or all mobs or can be combined with other challenge runs such as No Rocket run or No IC2 Crop Breeding.
This guide is all from my current experience so there may be changes across versions as I have kept up or fallen behind development. I will try to keep it as close to up to date as possible though.
Quick Overview of Major Obstacles
While the early game is largely unchanged progression-wise the first divergence I noticed was with getting into Thaumcraft. To get into Thaumcraft you need a wand and a wand needs Naga Scales. Naga scales normally come as a drop from Nagas but in this challenge you either need to get a [Profane Wand] or you need to get a Naga Bee. You also need to get some Thaumium in order to craft the Naga Scale Fragments and Chips from the Naga Bee into full Naga Scales. Because we cannot craft thaumium without a wand we need to get thaumium from [dungeon chests]. It is rare but very possible.
The next major divergence is with Nether Stars. The inability to summon and kill a wither means we must go a long time without any nether stars and there are whole mechanics that are locked out until then such as the Nasa Workbench which is needed for space travel even to the moon. My solution to this problem is... still to be determined.
Because we are stuck in, effectively, a No Rocket Run we must reroute our acquisition of every resource that would normally be acquired through planetary progression. The first of these is Titanium. This can be gotten initially from Andradite which has several sources available to us and shortly after from Stone Dust processing.
The next metal I noticed was Neodymium but luckily, depending on which method you used to get your early Andradite, you should already have some of the necessary ingredient to make it. Neodymium can be gotten by processing Sluice Sand in an Electromagnetic Seperator in HV. Sluice Sand can be gotten from Sluice Juice in a distillery and Sluice Juice is gotten by processing one of 6 dusts with nitric acid in a centrifuge. All six of those dusts are available to us in the overworld.
Another metal I noticed having difficulty sourcing was Tungsten. Tungsten is normally gotten with either Endstone Dust or Moon Stone Dust. Because of our lack of nether star we cannot get to the moon and because returning from the End with Endstone Dust would require killing the ender dragon (which I considered to be against the spirit of the challenge even if not against the defintion of "stay in peaceful mode") we need another route to get Tungsten or one of those dusts. Luckily we have a few reroutes; Ender Saplings from Thaumic Bases can let us get our first end stone without ever setting foot in the End or on the moon or we can process Pahoehoe Lava in a Centrifuge using the EV recipe to get Sheelite which can be processed into tungsten.
Reroutes
During a Peaceful Challenge run we will need to perform several reroutes to access some mechanics.
Thaumium/Wand
Your first Thaumcraft Wand is normally crafted using Naga Scales which are gotten as a drop from fighting the Naga in the Twilight Forest. We cannot fight the Naga so we must aquire either a Wand without Naga scales or Naga scales without fighting the Naga and luckily for us both are possible.
The simpler option is to find a Heretic villager and buy a Profane Wand. This has the downsides of a Profane Wand though including the Warp and the limited capacity and functionality.
The more complex option but the one you will eventually want to go for if you want to engage with thaumcraft requires bees. Using Naga, Lich and Hydra Bees we can get Naga Scales, Lich bones and Fiery Blood without fighting any of the bosses. A downside to this is that you need at least 3 thaumium to craft the Naga Scale Fragments into Naga Scales before you can craft the first wand. You can get these three thaumium from a dungeon chest or you can use a profane wand from the first method to craft them.
Titanium
Because we can't get nether stars we cannot go to any other celestial bodies. This means that we must reroute Titanium and some other metals that would conventionally be sourced from these other dimensions.
Titanium can be sourced from Andradite which itself has multiple sources in the overworld. I found that Yellow Garnet from Garnet Sand in Garnettin Veins was a reasonable source for me but you can also use Calcite Ore processing from Lapis Veins or Andradite Ore itself from Dolomite Veins.
I would advise moving away from those methods of sourcing Titanium fairly quickly though since passive Titanium can be gotten by processing Stone Dust.
Neodymium
Neodymium is fairly simple to reroute (if it even is a reroute but whatever) by processing Sluice Sand in an Electromagnetic Seperator in HV. Sluice Sand is gotten from Sluice Juice which is gotten from processing one of six dusts in a centrifuge with Nitric Acid.
Tungsten
Tungsten is conventionally sourced from Endstone or Moon Stone. We don't have conventional access to these resources so our alternatives are Ender Trees from Thaumic Bases or Pahoehoe Lava Processing. Pahoehoe Lava centrifuging has two recipes and we can't get EV Energy Hatches to run the IV recipe without Tungstensteel but we can run the EV recipe without them. Ender trees will turn the top layer of ground underneath their leaves into end stone and obsidian for around a dozen blocks. You can move the leaves using shears if you want to spread them out and they will still work.