Hmm... Couple thoughts.
Monk seems appealing because of how many kids points you can get. I think a monk probably would be able to use abundant step the most. You could use ascetic style to still have a sword, and fast movement helps sell the extremely fast. Bonus feats are also nice.
Alternatively you could pick a 3/4 caster. Magus gets nice bonus feats, so does occultist with that one combat archetype. Don't remember if occultist get Wizard spells are not. Not that many uses though, and a bit late.
What about full casters? To my knowledge dimension door isn't available to divine casters (with an acceptable combat BAB) but the halcyon druid archetype gives some Wizard spells. Maybe some cleric domain gives dimension door. This gives you some healthy BAB and spellcasting.
Edit: Unchained monk gets abundant step as early as 8th level.
Hmm...
Well I would use a temple sword or nine ring broadsword and then ascetic style. (Maybe GM is willing to reskin?)
All left over feats for the dimensional agility family.
Maybe extra ki? Staple power attack? Stuff like that? Really just pick up any monk guide.
I just realized you get flurry of blows to use with dimensional assault... Yeah this character sounds super badass.
It sounds like you want an Ancient Lorekeeper Oracle. Elf or Half-Elf exclusive Archetype where you pick your Oracle bonus spells from the Wizard list. Extremely strong in general, perfect for an "assassin" with all the arcane magic.
Other options for casting Dimension Door include Clerics with Travel Domain, Shamans with Lore Spirit, or Eldritch Knights (or similar Prestige Class arcane builds) built for combat.
Any character can get Dimension Door as a WIS-based Spell-like Ability with 3 levels of Horizon Walker.
Honestly, Monk is kind of a poor fit for Dimensional Dervish, since they already have Flying Kick. Dimension Door is usually just going to waste their Ki Pool and eat their swift actions when they could have just jumped the target.
Edit: The arcane spell Sense Vitals grants Sneak Attack by helping strike vital organs, which would be perfect. Combo with Dazzling Blade and/or Dimensional Savant.
You can always go bard, magus, mesmerist, occultist, skald, spiritualist (phantom blade, probably), or summoner, instead of monk; possibly with a dip in swashbuckler for the "swordsman" concept (inspired blade to qualify for Fencing Grace immediately is an attractive option). Dimension door is on all of those spell lists (as a 3rd-level spell with the APG summoner). Arcanist, sorcerer, or wizard/eldritch knight may also be an option.
Example of a bard. Note that Dimensional Agility was not a central part of this character concept, but Dimensional Dervish + dance of a thousand cuts is pretty nice.
The Flickering Step feat can provide a few additional shots of dimension door for relatively minimal investment, in addition to making feat access easier with a high-level fighter splash. ^_^
Arcane trickster wizard might be another way to reach DimDoor rather fast. A Dex build with TWF and sneak attack might be what you're looking for. Feat intensive though.
Some notes on Ancient Lorekeeper: Kindred-Raised Half-Elf can have +2 to both charisma and strength, which is perfect for a melee Oracle. Lore, Nature or Lunar Mystery can substitute charisma for dexterity when calculating dodge AC. So a kindred-raised Half-Elf could run something like: 16/18STR, 10DEX, 14CON, 10INT, 8WIS, 15/17CHA, and wear mithral medium armor with a huge "DEX" bonus on top of it. Basically, you get to use lighter armor as if you had a DEX-based character, while still using two-handed STR katana.
One way to do Ancient Lorekeeper would be to grab one level of Snakebite Striker Brawler and take Accomplished Sneak Attacker for 2d6 Sneak Attack. Then you can specialize in the arcane spell Dazzling Blade to throw blind on enemies while using the Oracle spell Divine Power for a huge combat buff, and the arcane spell Heroism for yet more accuracy. Put all together, with one round to prep Persistent Dazzling Blade and cast Divine Power, you get at least +6 to attack bonus from Divine Power, Fate's Favored and a blind enemy. The damage bonus vs. a blind target is +4 from Divine Power and +2d6 Sneak Attack, on top of high strength and Power Attack.
So for an "assassin" theme, you prepare a huge combat buff and set your katana glowing with mesmerizing light, then Dimension Door over to a target, blind them with a burst of light from your sword, and cut them down with rapid teleporting katana strikes that score a Sneak Attack bonus. Anything trying to hurt you has to deal with mithral armor and very strong Dodge bonus, plus maybe Mirror Image if that's one of your arcane spell picks. And besides everything else you're still a strong Oracle spellcaster for things like Burst of Radiance if you want.
Flickering Step is great, but very, very limited uses/day.
I'd consider normal Rogue/ Weapon Master/ Horizon Walker if going without spells. Weapon Master gets the good Fighter weapon stuff quickly, including Advanced Weapon Training stuff. Non-unchained Rogue can get a Ninja Ki Pool for Vanishing Trick and/or Shadow Clone, and use the Scout and maybe Thug Archetypes. Both Horizon Walker Dimension Door and Rogue Ki Pool use WIS.
Is this a character who can use Retraining? If you can, it doesn't matter so much when you actually get Dimension Door. If you can't, you might want a build that grabs it as soon as possible.
Depends on whether you want a STR or DEX character, and whether you want two-handed or two-weapon, and whether an elven curved blade is an acceptable alternative to a katana.
Well, two-handed curved blade with Power Attack works nicely with something like 14STR, 15/17DEX, 14CON, 10INT, 14WIS, 8CHA. Agile weapon is useful, though it's stronger to grab Trained Grace once you have Weapon Master 4, doubling the Weapon Training and Gloves of Dueling bonus to +6 and keeping more weapon enhancement.
You could probably also use something like 15/17STR, 16DEX, 12CON, 10INT, 12WIS, 9CHA if the idea of dual wielding katanas appeals to you; I think the feats are there to do it well enough. There are two ways to drop the penalty for dual wielding larger weapons, and one is pretty cheap. DEX AC is a bit lower, but Advanced Weapon Training and some mithral medium armor is still pretty decent.
Edit: come to think of it, you can Finesse dual katanas with Weapon Master. Not sure how well that would come together on a build like this, but it would probably work ok.
Effortless lace, duelist's vambraces, the hand's autonomy feat and/or the effortless dual-wielding advanced weapon training. I'm not sure which are the two you mean BadBird but there's options there. I'd go with effortless lace (and hand's autonomy if I could spare the feats) personally.
I was thinking of Effortless Lace or Advanced Weapon Training: Effortless Dual Wield, but forgot about those others. Lace is cheap even if eventually put on both weapons with a spare in pocket.
How to spread levels is pretty flexible. The first 11 levels should go Weapon Master 4, Rogue 4, Horizon Walker 3, but what comes first depends on what abilities you want first.
Weapon Master gains the ability to take the Advanced Weapon Training feat twice at Weapon Master 4: once from the level 4 bonus feat, once from replacing their level 2 bonus feat (with the free Fighter retraining ability, not with the optional Retraining rules system). How much they matter depends on the build.
Rogue 4 means you get the second Rogue Talent pick. You can always take the Extra Rogue Talent feat earlier than this, and you can always use a Rogue Talent feat to take a combat feat, so Rogue 4 is basically just about an extra feat/talent.
Horizon Walker 3 gets the Dimensional Dervish chain started sooner, which is obviously important if you can't use Retraining rules to grab the chain when you want to.
Edit: just looking at Ki Pool, even with no CHA, Ninja can work as well as Rogue. They're pretty much interchangeable, depending on what perks you want.