Tartaglia "Childe" boss fight happens near the end of the Archon quest in Liyue. He is part of the main story boss that you will inevitably fight, and will later be unlockable as part of the weekly bosses that you can do in the game.
You need to finish the Archon quests related to Liyue all the way to the end, until you fight him in the story mode to unlock this. The lowest difficulty starts at Adventure Rank 35 where the boss is at level 60. Picking up the rewards costs 60 resin, similar to the other weekly boss. You can only claim the rewards from him once a week, that resets every weekly server reset.
Who you use for your main damage dealer to get to this point will still work just fine. This is because even though Tartaglia can do Hydro and Electro elemental attacks, he can still take damage from those elements. He does have Hydro shield in phase 1, and Electro shield in phase 2, if you are attacking in melee, so it's better to go with other elements, but it's not really a big issue.
Since it's quite an extended fight, you will most likely want to bring 1 or 2 healers in the party. Bennett is a great option since his elemental burst can help get rid of Riptide mark as well as heal and atk increase. Defenseive characters like Diona, Noelle, Beidou, or any Geo characters to get a shield can help mitigate some damage if you are not good at dodging.
Since Tartaglia mostly attacks with either Hydro, and Electro (2nd and 3rd phase), you can craft some potions to increase your entire party's elemental resistance. You can craft these at the crafting table that's available in all the cities. Be sure to craft these using Lisa, since she has a passive that will has a chance to partially refund used materials.
However, do keep in mind that you can only have 1 active potion at a time. Consuming multiple potions at the same time will not work. Only 1 potion effect, and it's the last one you use, will be the one that persists.
During the fight, a lot of Tartaglia's attack will cause the "Riptide" mark on you. This mark will not do anything by itself, but if you get hit with certain follow up attack, the mark will detonate and deal massive hydro damage to you. This mark lasts quite a while, and also persists even when you switch out your character.
You are able to remove the mark by inflicting yourself with a Pyro element, and causing a "Vaporize" reaction. You can do this with characters like Bennett's elemental burst. If you don't have any Pyro element, you can touch the outer walls of the area. It will inflict you with a Pyro element, causing Vaporize and removing the mark.
Starting the fight, Tartaglia will always start with his "basic attacks," which are his string of aqua shots with his bow, and the water waves. This is to try and apply the Riptide mark on you. If you are not hit with a mark, he will often spam the basic attacks relentlessly.
This is his bow charged shot. Targets your location and continuously fires a hydro arrow that explodes in an area. He will only start doing this when you are marked. If you are hit with this attack, it will detonate your Riptide mark and deal massive damage.
This is his widest area attack that he can do. Tartaglia will start charging his bow from afar and summons a whale that flies into the air and dives into the ground, creating a large splash and dealing massive damage as well as detonating your Riptide mark. You can avoid this attack by getting close to Tartaglia, or not getting close to the dive splash.
Once you deplete his health the first time, Tartaglia will go to the center, envelop himself in water, and transform into his second phase. You are able to get some quick hits the moment his HP bar shows up during the transformation process.
Similar to the first phase, he will start to use his "basic attacks" to try and mark you. Except in the second phase, he no longer uses a bow, and will constantly charge at you through various attacks. If you see him take out his spear, he will do 2 to 5 thrust attacks. If he dashes towards you, it's often followed by a series of slashes. You might have an easier time going against him if you are using a ranged main damage dealer.
If you are marked with Riptide, Tartaglia will target you with an Electro ring from afar. After a few seconds, he will do a thunder strike from the air, dealing big damage twice. You can avoid this attack by touching the wall and getting rid of the mark, even if the Electro ring is already on you.
In his third phase, he has a lot more variety to his "basic attacks." If you are ranged, he has 4 different ranged attacks to target you from afar. Though, almost all of them are fairly telegraphed and can be easily avoiding by side stepping even without dashing.
His melee attacks are also quite slow and noticeably telegraphed. Stick close to him if you are melee, and if you see him about to attack, go to his back. If he is about to do a back sweep when you are behind him, rotate to his front.
If you are marked by the riptide, he has a chance to use his ultimate ability. Tartaglia will charge for a few seconds, and shoots down multiple arrows with huge AOE, and deals massive damage. You can avoid this by going to the center of the area, or the outer edges of the area that has gaps between the circles. Otherwise, you can always remove the marks by touching the walls before he uses his ultimate.
He can also summon the whale attack if you are marked. But there is no difference between the third phase whale to the previous ones.
The rewards that he drops are the same as the other weekly bosses, except for the elemental ascension materials. However, at Adventure Rank 40 (Boss level 70), Tartaglia will start dropping the boss exclusive materials. The materials are usually used for levelling your talents. Higher boss levels don't have anything new, so presumably they just have higher rates for the better rewards.
If you managed to win the fight without getting hit with his unique attacks that detonate your mark, you will get the achievement: "Outlander Vs. Outlander".