Kimahri's Celestial Weapon - Spirit Lance
As with all the Celestial Weapons in the game, Kimahri's will first require you to obtain the Celestial Mirror which lets you power up weapons as well as open the chests that contain them. Once you've acquired the mirror your next task will consist of finding the following three items; Spirit Lance, Saturn Sigil and Saturn Crest.
Let's start with finding the Spirit Lance. For this I highly recommend you acquire an item with [No Encounters] on it. You can add the ability to an item via Weapon Customization or you can find an item that has it from killing in Omega Ruins or some other high level area. Once you're ready board the airship and take it to the Thunder Plains.
Once you arrive in the Thunder Plains you're going to be looking for Cactuar stones that are glowing. You'll need to pray at one in the first field of Thunder Plains and two in the second. One of them in the second is located in an alcove and is a static spawn. The others rotate throughout the field.
After you pray at all the Cactuar statues that you need to you'll see a ghost cactuar in the second field which will lead you two a large statue which you must pray at. Do this and you'll make a chest appear which has Kimahri's Spirit Lance inside of it.
This item is commonly grabbed on your playthrough of the game so you may want to check your Key Items to see if you have it prior to wasting time heading to Mount Gagazet. If you don't have it in your inventory already then take the airship to Mt. Gagazet and take the teleporter nearby to "Mountain Trail" on the list of locations.
From here you'll want to follow the path as you would normally to the north until you reach an area with pillars. At this area of pillars inbetween the middle pillars on the left hand side you'll find the Saturn Crest.
The Saturn Sigil is the real pain in the arse item to get for Kimahri's Ultimate Weapon. For this you'll need to complete the butterfly hunt minigame in Macalania Woods... twice. If you haven't acquired the [No Encounters] ability you need to do so now.
You will need to complete both of the different Butterfly Hunts in the Macalania Woods - there's one in the northern part and one in the central part. If you're unfamiliar with how this game works you have to 'touch' the blue butterflies while avoiding the red ones.
I found this to be the most difficult of the minigames to do as far as acquiring the Ultimate Weapons go. There are a lot of different maps and videos online that will help you complete this minigame. Here is a link to one of the videos that I found helpful for completing this minigame!