Pirate bosses are Raiding ship bosses.
To get them to spawn and come after you, you need to carry Trader Goods that are the same as or higher the bosses’ levels.

Example:
To spawn a Falcon level boss, you should carry a LvL 6 Trader Good in your ship.
BUT, if your ship is lower, say LvL 4, then carrying LvL 8 Trader Good would increase chances.
If your ship is higher LvL, the bosses may still spawn even with lower level Trader Goods. [source]

PS: Same LvL pirates ship should drop these drawings also
You will only give drawings if u board them

‡Pirate LvL‡ Pegleg -> IronHand -> SteelTooth -> GoldenEye -> Jackal -> Falcon -> Flying Tiger -> Skeleton -> Devil -> Hades

PS: Flag ships in all the Battlefields also drop drawings

I added bosses’ stats, nationalities and avatars for your references, but the data is unconfirmed.
Sources for the data are from here & here (both in Chinese) –Feist

‡ Barbarossa II ‡ Wikipedia link

LvL 4 GoldenEye boss Nationality: Crete Pirate

Ship Stats
Sailors: 417
Hull: 4615
Sail: 14957
Square Sail Propulsion: 89
Triangular Sail Propulsion: 19
Oar Propulsion: 0

Boss Stats
Grapple: 230
HP: 602
ATTK: 45
DEF: 30
ATTK Speed: 2000
Hit Rate: 121
Dodge Rate: 41

Place
(top left corner of Crete island) turning point where u go to Venice from Athens. near -229 -213, spawns every 20 minutes

“It's not easy to fool Barbarossa, but it's worth the time.
First thing, he mostly comes out at night when the patrol ships and the frigates go to re-supply.
Secondly, he doesn't have a spawn point. He just picks up merchants that seem easy targets.
So try to act as one. Move around, especially on the Venice-Alexandria trade route (check during day to see where the traders turn to pass Crete).
He will eventually show up, guns blazing, and grapple you before you get to say meow.” [source]

Drops
◊ LvL 31 Lieutenant Command weapons and other lv31 weapons
◊ LvL 4 ship drawings: (all type) Lion figurehead drawings, (all type) shields

‡ Emanuel Wynne ‡ Wikipedia link

LvL 5 Jackal boss Nationality: North Sea Pirate

Ship Stats
Sailors: 525
Hull: 6433
Sail: 20422
Square Sail Propulsion: 95
Triangular Sail Propulsion: 20
Oar Propulsion: 0

Boss Stats
Grapple: 300
HP: 798
ATTK: 55
DEF: 40
ATTK Speed: 2000
Hit Rate: 130
Dodge Rate: 50

Place
Amsterdam <-> London route, near 115 -585, spawns every 25 min

Drops
◊ LvL 41 Lieutenant Commander Command weapons
◊ LvL 51 Commander Command weapons
◊ LvL 5 ship drawings: (all type) Beluga figurehead drawings, (all type) shields

‡ Don Esteba Caterina ‡ nick: queen of pirates or sumthing xD

LvL 6 Falcon boss Nationality: Kingdom of Spanish

Ship Stats
Sailors: 689
Hull: 9466
Sail: 29215
Square Sail Propulsion: 101
Triangular Sail Propulsion: 21
Oar Propulsion: 0

Boss Stats
Grapple: 440
HP: 1468
ATTK: 76
DEF: 51
ATTK Speed: 1000
Hit Rate: 121
Dodge Rate: 59

Place
Seville <-> Lisbon route, near 303 -197, spawns every 30 min

Attacking her will cost your amity with Spain: -6 every shot. [source]
She has spawn on players with Portuguese or English nationality.
She probably won’t spawn / attack you if you are a citizen of Spain. [source]

Drops
◊ LvL 41 Lieutenant Commander Command weapons
◊ LvL 51 Commander Command weapons
◊ LvL 6 ship drawings: (all type) Falcon figurehead drawings, (all type) shields

‡ William Dampier ‡ Wikipedia link

LvL 6 Falcon boss Nationality: South Sea Pirates

Ship Stats
Sailors: 689
Hull: 9466
Sail: 29215
Square Sail Propulsion: 101
Triangular Sail Propulsion: 21
Oar Propulsion: 0

Boss Stats
Grapple: 440
HP: 1468
ATTK: 76
DEF: 51
ATTK Speed: 1000
Hit Rate: 121
Dodge Rate: 59

Place
Malacca <-> Semarang route, near -1498 392 , spawns every 30 min

Drops
◊ LvL 41 Lieutenant Commander Command weapons
◊ LvL 51 Commander Command weapons
◊ LvL 6 ship drawings: (all type) Falcon figurehead drawings, (all type) shields
　　

‡ Ali Rajah ‡
“Ali Raja” is a Muslim name for Indonesian pirates, means “King of the Sea” [source]

LvL 7 Flying Tiger boss Nationality: South Sea Pirates

Ship Stats
Sailors: 941
Hull: 14644
Sail: 43931
Square Sail Propulsion: 137
Triangular Sail Propulsion: 22
Oar Propulsion: 0

Boss Stats
Grapple: 720
HP: 2114
ATTK: 122
DEF: 81
ATTK Speed: 2000
Hit Rate: 151
Dodge Rate: 71

Place
Sri Lanka left bottom corner, near: -1034 326 , spawns every 35 min

Drops
◊ LvL 61 Captain Command weapons
◊ LvL 7 ship drawings: (all type) Mermaid figurehead drawings, (all type) shields

‡ Klaus Störtebeker ‡ Wikipedia link
[source]

LvL 7 Flying Tiger boss Nationality: North Sea Pirates

Ship Stats
Sailors: 941
Hull: 14644
Sail: 43931
Square Sail Propulsion: 107
Triangular Sail Propulsion: 22
Oar Propulsion: 0

Boss Stats
Grapple: 720
HP: 2114
ATTK: 122
DEF: 81
ATTK Speed: 2000
Hit Rate: 151
Dodge Rate: 71

Place
North Sea, Stockholm <-> Oslo route, near -21 -646, spawns every 35 min 　　

Drops
◊ LvL 61 Captain Command weapons
◊ LvL 7 ship drawings: (all type) Mermaid figurehead drawings, (all type) shields

‡ Thomas Tew ‡ Wikipedia link
[source]

LvL 8 Skeleton boss Nationality: Aden Pirates

Ship Stats
Sailors: 1207
Hull: 21243
Sail: 64584
Square Sail Propulsion: 113
Triangular Sail Propulsion: 23
Oar Propulsion: 0

Boss Stats
Grapple: 840
HP: 2553
ATTK: 139
DEF: 98
ATTK Speed: 2000
Hit Rate: 160
Dodge Rate: 80

Place
Aden gulf, near -678 193, spawns every 40 min

Drops
◊ LvL 71 Rear Admiral Command weapons
◊ LvL 8 ship drawings: (all type) Angel figurehead drawings, (all type) shields

‡ Francis Drake ‡ Wikipedia link

LvL 8 Skeleton boss Nationality: Kingdom of England

Ship Stats
Sailors: 1207
Hull: 21243
Sail: 62584
Square Sail Propulsion: 113
Triangular Sail Propulsion: 23
Oar Propulsion: 0

Boss Stats
Grapple: 840
HP: 2553
ATTK: 139
DEF: 98
ATTK Speed: 2000
Hit Rate: 160
Dodge Rate: 80

Place
Bordeaux <-> Lisbon route, near 256 405 , every 40 min

Drops 　　
◊ LvL 71 Rear Admiral Command weapons
◊ LvL 8 ship drawings: (all type) Angel figurehead drawings, (all type) shields

‡ Murayama Tōan ‡ Wikipedia link
[source]

LvL 9 Devil boss Nationality: Japan

Ship Stats
Sailors: 1450
Hull: 29099
Sail: 84531
Square Sail Propulsion: 118
Triangular Sail Propulsion: 25
Oar Propulsion: 0

Boss Stats
Grapple: 1100
HP: 3451
ATTK: 189
DEF: 123
ATTK Speed: 2000
Hit Rate: 169
Dodge Rate: 89

Place
Above Taiwan near -1801 -48, spawns every 50 min

Drops
◊ LvL 81 vice Admiral Command weapons
◊ LvL 9 ship drawings: (all type) Titan figurehead drawings, (all type) shields

‡ Hilton Laces ‡

LvL 9 Devil boss Nationality: Corsica Pirates

Ship Stats
Sailors: 1450
Hull: 29099
Sail: 84531
Square Sail Propulsion: 119
Triangular Sail Propulsion: 0
Oar Propulsion: 25

Boss Stats
Grapple: 1100
HP: 3451
ATTK: 189
DEF: 123
ATTK Speed: 2000
Hit Rate: 169
Dodge Rate: 89

Place
Sardina island left bottom corner, spawns every 50 min

Drops
◊ LvL 81 vice Admiral Command weapons
◊ LvL 9 ship drawings: (all type) Titan figurehead drawings, (all type) shields

‡ Edward Teach (aka Blackbeard) ‡ Wikipedia link

LvL 10 Hades boss Nationality: Gibraltar Pirates

Ship Stats
Sailors: 1450
Hull: 37951
Sail: 109254
Square Sail Propulsion: 125
Triangular Sail Propulsion: 26
Oar Propulsion: 0

Boss Stats
Grapple: 1400
HP: 4683
ATTK: 297
DEF: 141
ATTK Speed: 1000
Hit Rate: 142
Dodge Rate: 98

Place
Place: around Dakar, near 475 109, spawns every 55 min

Drops
◊ LvL 91 Admiral Command weapons
◊ LvL 10 ship drawings: (all type) Neptune figurehead drawings, (all type) shields

　　
‡ William Kidd ‡ Wikipedia link

LvL 10 Hades boss Nationality: Cape of Good Hope Pirates

Ship Stats
Sailors: 1450
Hull: 37951
Sail: 109254
Square Sail Propulsion: 125
Triangular Sail Propulsion: 0
Oar Propulsion: 26

Boss Stats
Grapple: 1400
HP: 4683
ATTK: 297
DEF: 141
ATTK Speed: 1000
Hit Rate: 142
Dodge Rate: 98

Place
around Cape Town, near -420 918 (DANGEROUS), spawns every 55 min

Drops
◊ LvL 91 Admiral Command weapons
◊ LvL 10 ship drawings: (all type) Neptune figurehead drawings, (all type) shields

　　
‡ Tokisada Amakusa Shiro ‡ Wikipedia link
[soure]

LvL 10 Hades boss Nationality: Ryukyu Pirates

Ship Stats
Sailors: 1405
Hull: 37951
Sail: 109254
Square Sail Propulsion: 125
Triangular Sail Propulsion: 0
Oar Propulsion: 26

Boss Stats
Grapple: 1400
HP: 4683
ATTK: 297
DEF: 141
ATTK Speed: 1000
Hit Rate: 142
Dodge Rate: 98

Place
Seoul <-> Nagasaki route, near -1838 -174, spawns every 55 min

Drops
◊ LvL 91 Admiral Command weapons
◊ LvL 10 ship drawings: (all type) Neptune figurehead drawings, (all type) shields

　　
‡ Oji ‡ Wikipedia link
[soure]

LvL 10 Hades boss Nationality: South Sea Pirates

Ship Stats
Sailors: 1450
Hull: 37951
Sail: 109254
Square Sail Propulsion: 125
Triangular Sail Propulsion: 0
Oar Propulsion: 26

Boss Stats
Grapple: 1400
HP: 4683
ATTK: 297
DEF: 141
ATTK Speed: 1000
Hit Rate: 142
Dodge Rate: 98

Place
below Tourane, near -1625 160, spawns every 55 min

Drops
◊ LvL 91 Admiral Command weapons
◊ LvL 10 ship drawings: (all type) Neptune figurehead drawings, (all type) shields

‡ Bartholomeus Roberts ‡

LvL ?? boss “Nightmare Level Armored ship” Nationality: ?

Ship Stats
Hull: ?
Sail: ?
Square Sail Propulsion: ?
Triangular Sail Propulsion: ?
Oar Propulsion: ?

Boss Stats
Grapple: ?
HP: 43305
ATTK: 592
DEF: 369
ATTK Speed: ?
Hit Rate: 264
Dodge Rate: 114

Place
Medeira <- Lisbon –> London route [soure], also seen near Luanda [soure], spawns every ?? min

Drops
◊ ??
◊ ??

‡ John Hawkins ‡ Wikipedia link
[soure]

LvL ? boss “Scared Level Armored ship” Nationality: ?

Ship Stats
Hull: ?
Sail: ?
Square Sail Propulsion: ?
Triangular Sail Propulsion: ?
Oar Propulsion: ?

Boss Stats
Grapple: ?
HP: 42644
ATTK: 573
DEF: 344
ATTK Speed: ?
Hit Rate: 300
Dodge Rate: 244

Place
(possibly) Luanda <- Accra – Dakar -> Madeira route [soure] [soure], been seen near 434, 313 [soure], spawns every ?? min

Drops
◊ ??
◊ ??