Judged by the following 3 the most
Awoken Skill - Does it have better Awoken Skill (such as Skill boost, 2 Pring, Attribute Enhance)
Skill - Number of turns it takes at max skill level, or how effective is the skill.
Leader Skill - Damage magnifiers, and ease of activation
S Rank - All 3 of above are very powerful. Vegito and Awoken Ra are very popular, as many color combo damage mangifiers are strong.
A Rank - All 3 of above are very powerful, but can be difficult to use (ease of use), or difficult to obtain ideal subs. However with the ideal team, is comparable to a S Rank.
B Rank - Very Strong leader monster, but composition of team is more difficult than A Rank. Pandora and other Hero series are very strong, but since it is difficult to beat recent dungeons with things such as combo absorb and other gimmicks, they are rank B.
S Rank
Awoken Ra
Vegito
Awoken Bastet
Juggler
A Rank
Light Kali
Awoken Parvati
Awoken Horus
Awoken Shiva
Gadeius
Ulti Goemon
Light Anubis
Awoken Lakschmi
Cloud (If Cloud System Part is Rank S)
Ulti Sarsvati
B Rank
Pandora
Wukong
Santa Sakuya
Verdandi
Urd
Skuld
Ilm
Sephiroth
Yuna
Soniagran
Subs
Subs are ranked based off 4 things. Skill, Awoken Skill, Status, and does Substitution Monster exist or not. Leader skill is not considered. I'm pretty sure Status means stats, no clue why Japanese people call it status.
Skill - Number of turns it takes at max skill level, or how effective is the skill.
Awoken Skill - Does it have better Awoken Skill (such as Skill boost, 2 Pring, Attribute Enhance)
Status - HP, Attack, RCV stats are all at least average, or otherwise has 1 Stat that is very high.
Substitution - Does it have any substitutes that you could use instead? Does it hold a unique skill that can't be replaced?
S Rank - Skill, Awoken Skill, Status are all very strong. No substitutions for that monster (is unique). Monsters with things such as 3x 2 Prongs, or stuff like Light Kali which has unique skills (not really sure what they meant by 固有スキル).
A Rank - 2 or 3 useful color orb changing skill. When compared to S Rank, it's awoken skill or status isn't as good. However, it has very little monster you can substitute it with and is very strong.
B Rank - Stuff like 5 turn orb conversion, double conversion, in general skills that are useful in tight situations. Can be used in many parties. Awoken Skills and status falls behind A rank monsters, and substitutes exist for this monster. Is a strong sub.
S Rank
Awoken Hinogakutschi
Liu Bei
Chibi Valkyrie
Baggi (monster hunter)
Dark Kali
Light Kali
A Rank
Red Sonia
Blue Sonia
Osiris
Ulti Sun Quan
Lei Lan
Karin
Meimei
Haku
Uld
Skuld
Verdandi
Ilm
B Rank
Fire Valkyire
Water Vaklyrie
Wood Valkyire
Dark Valkrie
Yomi
Pandora
Yamato Tkaeru
Andromeda
Perseus
Wukong
Dark Izanami
Ares
Hermes
Apollon
Persephone