The 
Seitengrat bow is an extremely powerful weapon added to the Zodiac Age and IZJS versions of the game. The bow has an attack power of 224 which puts it significantly above the attack power of all other weapons, including two-handed swords.
The RNG manipulation method does not work on the Nintendo Switch version of the game.
The Seitengrat appears in a treasure chest that spawns on the top deck of the Skyferry. There is a 1% chance that an invisible chest will spawn. This chest has a 20% chance of containing an item and an 80% chance of containing 10 gil.
The item that it contains is typically a Knot of Rust, however, with the Diamond Armlet equipped, there is a 5% chance that this item will be the Seitengrat bow. Altogether, the odds of obtaining it are:
This is equivalent to 1 in 10,000. In other words, this item was designed to be extremely rare and to be next-to-impossible to obtain without a tedious amount of grinding or just plain getting lucky.
That being said, there is a way to obtain the bow by manipulating the game’s “random number generator” (RNG) engine to guarantee that you obtain the treasure chest.
Note that this method is borrowed from a method outlined by LetsGetPitted in his YouTube video here: https://www.youtube.com/watch?v=1VpFs1O8s9I. I have included an outline in this guide but full attribution goes to the hard work put together on this method by LetsGetPitted.
Additionally, resources were pulled from a number of subreddit posts in the Final Fantasy XII subreddit found here: https://www.reddit.com/r/FinalFantasyXII/
This method for obtaining the Seitengrat offers 100% success rate in the PlayStation 4 version of the game, however it requires that you follow a very specific set of steps in order to manipulate the RNG, which is a system that the game uses to determine whether treasure chests spawn and what they will contain (among a myriad of other variables that the RNG is responsible for).
To get started, open up the start screen of the game and choose to start a new game. This new game will only be used to manipulate the RNG; the Seitengrat will be obtained in your main game, however this new game is used to ensure that all of the appropriate steps are followed as it removes most of the other variables that would normally be at play.
Play through the start of the game until you reach the Save Crystal on the second floor as shown in the screen shot below.
You must travel up one floor past this and defeat the three Imperial Swordsmen past the Save Crystal as this will cause the NPCs that would normally appear near the Save Crystal to disappear. If the NPC are still on this floor they will have an impact on the RNG manipulation steps as they can manipulate the RNG themselves.
Save your game at the Save Crystal and then open up your main game file. Make sure that you have a Diamond Armlet in your inventory.
Check out the 
Diamond Armlet section of the Accessories page for more information. The easiest way to obtain one is in Trial Mode – Stage 1 by opening the treasure chest on the upper floor.
Use the Moogling transport to travel to Westgate. Head in to the Aerodrome and choose to travel to Nalbina using the airship (select the “By leisure craft” option, not the “By private cabin” option).
Make sure that Vaan has a Diamond Armlet equipped and then enter the deck of the airship on the upper level.
This should cause your PlayStation 4 to auto-save your game at this point (you will be able to see the icon in the top left corner of the screen). You will need this auto-save to get back up to the airship later.
Press and hold the 
Button and choose the option to “Close Application”. This will close out the game and will cause the RNG to completely reset. Now re-open the game and load up the “Nalbina Fortress / Upper Apartments” save file that you recently created.
You must now have Reks use the 
Cure Magick spell over and over again until you see a specific pattern. As you do this, you may need to refill your MP, so just touch the Save Crystal again if required.
Do not leave this area or it will affect the RNG and will cause an auto-save to save over your airship auto-save file.
You are looking for Cure Magick to heal you for three very specific HP amounts in a very specific order. You need to see:
88 – 97 – 90
You need to have these three numbers appear in this exact order. If you see 88, but 97 does not follow it, keep going until you see another 88. Once you see 88, 97 and then 90, stop casting Cure Magick at this point.
You now need to press the 
Button and choose the “Quit to Title” option by pressing the Square button. Do not “Close Application” like we did last time. You need to stay in the game in order to maintain the current manipulated RNG configuration.
This last step involves a little bit of timing so make sure that you read ahead and are familiar with the steps or watch the video below. Load up your auto-save which has Vaan on the deck of the airship.
Run up to the top of the deck and search for an invisible treasure chest by walking directly forward and you should run in to what appears to be an invisible wall. This is how you will know that the chest has properly spawned.
The last step involves a little bit of timing. You need to watch for an NPC who is on the stairs on the right side named the “Boonswaggled Bookkeeper”. This NPC starts on the middle landing of the stairs and will climb the stairs around the corner, before returning back to the landing again.
You need to wait until the NPC has climbed the stairs 3 times and on the fourth climb, open the treasure chest exactly when the NPC reaches the top step. This timing is fairly forgiving, but it needs to be right at the top step or just as he begins to turn the corner.
This will guarantee that the treasure chest contains the Seitengrat bow and you can repeat this method as many times as you would like.
Check out the following video to see a demonstration:
