List of Modules

No.		Japanese	English
1		初音ミク	Hatsune Miku
2		メイコスタイル	Meiko Style
3		リンスタイル	Rin Style
4		スペチャン5	Space Channel 5
5		スペチャン39	Space Channel 39
6		ガリア軍第7小隊	Gallia Squad 7
7		チア	Cheer
8		プラグイン	Plug-in
9		ゴシック	Gothic
10		プリンセス	Princess
11		ミコ	Miko
12		にゃんこ	Cat Girl
13		ねむねむ	Sleepy
14		ハートハンター	Heart Hunter
15		ボーカル	Vocal
16		パンク	Punk
17		ダンサー	Dancer
18		スター	Star
19		フェアリー	Fairy
20		スクール	School
21		スノウ	Snow
22		アラビアン	Arabian
23		みやび	Elegant
24		チャイナ	China
25		マジシャン	Magician
26		ホワイトドレス	White Dress
27		パイレーツ	Pirate
28		VN02	VN02
29		ギャラクシー	Galaxy
30		初音ミク スイムウェアS	Hatsune Miku Swimwear S
31		初音ミク スイムウェア	Hatsune Miku Swimwear
32		ハツネミク	Ha2ne Miku
33		P-スタイルPB	P-Style PB
34		P-スタイルCW	P-Style CW
35		P-スタイルIS	P-Style IS
36		P-スタイルRP	P-Style RP
37		P-スタイルLP	P-Style LP
38		P-スタイルFB	P-Style FB
39		P-スタイルMG	P-Style MG
40		P-スタイルCG	P-Style CG
41		弱音ハク	Yowane Haku
42		亞北ネル	Akita Neru
43		咲音メイコ	Sakine Meiko
44		メイコ	Meiko
45		メイコ スイムウェア	Meiko Swimwear
46		鏡音リン	Kagamine Rin
47		鏡音リン スイムウェア	Kagamine Rin Swimwear
48		鏡音レン	Kagamine Len
49		鏡音レン スイムウェア	Kagamine Len Swimwear
50		カイト	Kaito
51		カイト スイムウェア	Kaito Swimwear
52		巡音ルカ	Megurine Luka
53		巡音ルカ スイムウェア	Megurine Luka Swimwear

How to unlock

Note : To unlock a module, both of its conditions must be fulfilled - however for most cases, the conditions can be completed separately, and you don't necessarily need to fulfill them both at the same time, or even under the same difficulty.
I.e. :
For "Heart Hunter", you only need to get at least one "Standard" rank on normal and a total of 5 clears (on ANY difficulty).
For "School", you only need to get at least one "Great" rank on normal and a max combo of 100 (on ANY difficulty).
For "White Dress", you only need to get a "Standard" rank at least once in Hard mode, and have high score of 300k+ (on ANY difficulty).
Exceptions are cases when you need to beat a certain song with a certain costume/character.

No.	Costume	Song	Condition 1	Condition 2
Pink Tag
14	Heart Hunter	ワールドイズマイン	NORMAL /STANDARD	Clear five or more times
9	Gothic	ひねくれ者	NORMAL /STANDARD	MAX Combo 100
16	Punk	恋は戦争	NORMAL /GREAT	Clear five or more times
20	School	その一秒スローモーション	NORMAL /GREAT	MAX Combo 100
26	White Dress	メルト	HARD /STANDARD	More than 300,000 high score
Blue Tag
17	Dancer	Far Away	NORMAL /STANDARD	Clear five or more times
21	Snow	ストロボナイツ	NORMAL /STANDARD	MAX Combo 100
8	Plug-In	Star Story	NORMAL /GREAT	Clear five or more times
29	Galaxy	Last Night, Good Night	NORMAL /GREAT	MAX Combo 80
15	Vocal	Packaged	HARD /STANDARD	More than 250,000 high score
Orange Tag
12	Cat Girl	雨のちSweet:*Drops	NORMAL /STANDARD	Clear five or more times
25	Magician	ミラクルペイント	NORMAL /STANDARD	MAX Combo 120
18	Star	フキゲンワルツ	NORMAL /GREAT	Clear five or more times
13	Sleepy	マージナル	NORMAL /GREAT	MAX Combo 130
2	Meiko Style	Dreaming Leaf-ユメミルコトノハ-	HARD /STANDARD	More than 212,000 high score
Yellow Tag
6	Gallia Squad 7 (Alicia)	荒野と森と魔法と歌	NORMAL /STANDARD	Clear five or more times
48	Kagamine Len	荒野と森と魔法の歌(レンver.)	NORMAL /STANDARD	MAX Combo 100
46	Kagamine Rin	荒野と森と魔法の歌(リンver.)	NORMAL /STANDARD	MAX Combo 100
27	Pirate	ハト	NORMAL /STANDARD	MAX Combo 110
28	VN02	moon	NORMAL /GREAT	Clear five or more times
19	Fairy	みくみく菌にご注意♪	NORMAL /GREAT	MAX Combo 110
11	Miko	いのちの歌	HARD /STANDARD	More than 150,000 high score
3	Rin Style	いのちの歌	Len ver. NORMAL /GREAT	Rin ver. NORMAL /GREAT
Sky Blue Tag
32	Miku Hatsune (OP version)	The secret garden	NORMAL /STANDARD	Clear five or more times
7	Cheerleader	Dear cocoa girls	NORMAL /STANDARD	MAX Combo 110
22	Arabian	天鵞絨アラベスク	NORMAL /GREAT	Clear five or more times
24	China	ラブリスト更新中？	NORMAL /GREAT	MAX Combo 110
23	Elegant	桜ノ雨-standard edit-	HARD /STANDARD	More than 200,000 high score
White Tag
10	Princess	恋スルVOC@LOID	NORMAL /STANDARD	Clear five or more times
52	Megurine Luka	Ievan Polkka	NORMAL /STANDARD	MAX Combo 100
43	Sakine Meiko	あなたの歌姫	HARD /GREAT	Use Meiko (Module 44)
44	Meiko	あなたの歌姫	NORMAL /STANDARD	Clear five or more times
41	Yowane Haku	えれくとりっく・えんじぇぅ	NORMAL /STANDARD	MAX Combo 120 or clear 5 times or more
42	Akita Neru	初音ミクの消失	NORMAL /STANDARD	More than 230,000 high score
50	Kaito	金の聖夜霜雪に朽ちて	NORMAL /STANDARD	Clear five or more times
5	Space Channel 39	みくみくにしてあげる♪【してやんよ】	NORMAL /STANDARD	MAX Combo 70
4	Space Channel 5	みくみくにしてあげる♪【してやんよ】	HARD /GREAT	Use Space Channel 39 (Module 5)
P-Style
36	P-Style RP (Rose Pink)	All pink tag songs	NORMAL /GREAT	None
38	P-Style FB (Felicia Blue)	All blue tag songs	NORMAL /GREAT	None
37	P-Style LP (Lavender Purple)	All orange tag songs	NORMAL /GREAT	None
39	P-Style MG (Mint Green)	All yellow tag songs	NORMAL /GREAT	None
34	P-Style CW (Ceramic White)	All sky blue tag songs	NORMAL /GREAT	None
33	P-Style PB (Piano Black)	All white tag songs	NORMAL /GREAT	None
35	P-Style IS (Ice Silver)	All songs	NORMAL /GREAT	None
40	P-Style CG (Champagne Gold)	All songs	HARD /GREAT	None
Swimwear
30	Hatsune Miku Swimwear S (School ver.)	"The secret garden" and "Dear cocoa girls"	NORMAL /GREAT (HARD will not unlock this module)	While using "Hatsune Miku Swimwear" (Module 31)
31	Hatsune Miku Swimwear	All Miku ver. Songs	NORMAL(HARD)/GREAT or STANDARD(5x) *	Use "Hatsune Miku" (Module 1)
45	Meiko Swimwear	All Miku ver. Songs	NORMAL(HARD)/GREAT or STANDARD(5x) *	Use "Meiko" (Module 44)
47	Kagamine Rin Swimwear	All Miku ver. Songs	NORMAL(HARD)/GREAT or STANDARD(5x) *	Use "Kagamine Rin" (Module 46)
49	Kagamine Len Swimwear	All Miku ver. Songs	NORMAL(HARD)/GREAT or STANDARD(5x) *	Use "Kagamine Len" (Module 48)
51	Kaito Swimwear	All Miku ver. Songs	NORMAL(HARD)/GREAT or STANDARD(5x) *	Use "Kaito" (Module 50)
53	Megurine Luka Swimwear	All Miku ver. Songs	NORMAL(HARD)/GREAT or STANDARD(5x) *	Use "Megurine Luka" (Module 52)

*NOTE :
Regarding swimwear, it seems the method is still not 100% clear for everyone, so here's some explanation to further clarify :

Which/how many songs do I have to do?
ALL the Miku songs, or in other words, ALL songs EXCEPT these four :
荒野と森と魔法の歌(レンver.)
荒野と森と魔法の歌(リンver.)
いのちの歌(レンver.)
いのちの歌(リンver.)
You CAN do them if you want, but you don't really have to, so it's a waste of time.

That's a total of 32 songs.

What character/costume do I have to use?
The default ones. For Miku, that's the 1st one on the list, or module No. 1. For Meiko, that's the "Meiko" module (No. 44), not "Sakine Meiko". Rin, Len, Kaito and Luka should be obvious since they don't have a choice.

When can I consider a song as "done" ?
Whenever ANY of these conditions happens while using your desired character :
-Clear on Normal/GREAT
-Clear on Hard/GREAT
-Clear on Normal/STANDARD five times
-Clear on Hard/STANDARD five times

You only need to fulfill ONE of these requirements PER song, it can be whichever you want, and you can mix them however you want (I.e., clear the first 15 songs on Normal/GREAT, clear the next 15 songs on Hard/GREAT, clear the remaining 2 songs with Normal/STANDARD five times, etc.).

I did all songs meeting the conditions and got nothing!
The game doesn't show you what songs you've cleared using who. To be 100% safe, it is recommended to not trust your memory and simply start fresh from the first song, and do ALL of them, regardless of whether you've done it before or not. Also, for the clears, ignore whatever number the song has and start counting fresh from this run.
It is also recommended to keep a - of your progress on paper to avoid confusion.