Pretty Guardian Sailor Moon - La Reconquista

00:46 Maiden / One-on-One / Memory

These are all Japanese genres of video games.

Maiden Games = Otomegee

Certain games marketed towards women, dating simulation games in particular.

One-on-One Combat Games = Kakutougee

Games that usually fight games where you control one character against an opponent.

Memory Games = Oboegee

Games that require the player to remember patterns, particularly shooting patterns in shoot
'em up style games.

00:55 Infinite Duplication

Duplicating things such as items in games in order to get the high score

01:07 CGs

Computer Graphics, stills often found in video games to collect

01:12 Speedrun

Making a game more challenging by trying to play through as fast as possible

03:34 Momoiro Clover Z

Momoiro Clover Z is a five (formerly six) member idol group, each with their 
own image colour. This group promoted this musical by releasing a special online download
cover of "Moonlight Densetsu". Here three of them appear as puns.

Kanako (Leader) - Red - Pun on Kanako and Akazukin (Little Red Riding Hood) 
to make Kanazukin.

Shiori - Yellow - Pun on Tamai (Shiori's family name) and Himawari (Sunflower) to make
Tamawari.

Ayaka - Pink - Pun on Aarin (Ayaka's nickname) and Robot to make Arlin Rob. 
This is an in-reference to when Ayaka cracked her shin in January 2014, 
unable to dance, she instead made appearances in
various robot costumes.

Momoka - Green - Pun on Momoka and Katori (Mosquito Repellent)

Reni - Purple - Not really a pun but seems to be an excuse for Reni to yell because she is Reni.

22:44 Fine, V

Nephri combined "Daijoobu" (It'll be fine) with "bui" (V) as in the V-sign, 
to make "daijoobui". 

26:32 Patterns

Usagi is talking about anime/manga/drama "patterns", these are similar to cliches but the 
connotations are not so negative. These are common sequences seen in Japanese media.

27:29 Annie

A reference to the titular orphan of the musical "Annie"

28:23 Youma, S & SS

S and SS (SuperS) are series from the original Sailor Moon anime 3rd and 4th respectively.
Each had their own specific monsters which were Daimon and Lemures. The original Sailor Moon
series had "Youma" but Baba is a "Lemures", she's basically telling Usagi that they're just
ignoring the system of the Dark Kingdom use Youma and she's just been hired part-time.

33:46 Shiritori

This is a word game where somebody players take the last syllable of the previous word
and use it to be the next one, when somebody accidentally picks a word that ends with 'n',
they lose the game. The joke is that Ami keeps saying Mathematical terms that all end with
"ki"

Ami: Sukein KankeishiKI (Skein Relations)
Zoi: KInniKU (Muscles)
Ami: KUreroo no HouteishiKI (Clairaut's Equation)
Zoi: KInoKO (Mushroom)
Ami: KOoshiiriiman no HouteishiKI (Cauchy-Riemann Equations)
Zoi: KIkoRI (Lumberjack)
Ami: RIkaachi no HouteishiKI (Ricatti's Equation) 
Zoi: KIrei (Beautiful)

36:03 Dummy Riding Hood

Ami has confused "Kanazukin" with "Bakazukin"

55:44 Rabbit of the Moon

A pun on her name Tsukino Usagi which sounds like "Rabbit of the Moon".

1:14:27 Come to Your Senses

Also known as "Tsuki to Chikyuu" (The Moon and Earth) the reason for the title change is
not clear.

1:22:58 I can't read these characters

Baba is talking about Chinese characters (kanji) which are used in Japanese. Since many
have multiple readings, unfamiliar combinations can be difficult even for native speakers.

2:00:54 Z!

This is Momoiro Clover Z's trademarks, the "Z pose".