What are the different monster attributes?

Solution 1:

The three most important imo are

Term         | Meaning                     
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Early Peaker | The Monster can reach a maximum level of 20       
Well-Grown   | The Monster can reach a maximum level of 30 to 60    
Late Bloomer | The Monster can reach a maximum level of 70 to 90              

The rest all make sense based on what they are called. Examples: Hearty means the monster will have a higher HP than a monster without it. Strong means a monster will have higher strength. Pinch Hitter means the monster can learn abilities that can be activated when in danger, etc.

There are some that are element+prone which means the monster is weaker against that element. Some are element+proof which means the monster has a strong resistance to that element or will learn resistance abilities for that element.

For completeness: As mentioned by Yuck, only the first three attributes define the monster. The fourth attribute has no in game effect for your monster and is there for fun. See Yuck's answer for more information.

Solution 2:

Early Peaker: maximum level of 20
Well Grown: max level 30 to 60
Late bloomer: max level 70 to 99
Hearty: high hp growth
Strong: high strength growth
Magical: high magical growth
Balanced: balanced parameter growth
Brainy: learns many abilities
Flameprone: weak to fire
Frostprone: weak to ice
Sparkprone: weak to lightning
Windprone: weak to wind
Flameproof: strong fire resistance or learns fire resistance abilities
Frostproof: strong ice resistance/learns ice resistance abilities
Thunderproof: strong lightning resistance/learns lightning resistance abilities
Windproof: strong wind resistance/learns wind resistance abilities
Meleeproof: strong physical resistance/learns physical resistance abilities
Manaproof: strong magic resistance/learns magic resistance abilities
Venomproof: strong poison resistance/learns poison resistance abilities
Fogproof: strong fog resistance/learns fog resistance abilities
Painproof: strong pain resistance/learns pain resistance abilities
Hexproof: strong curse resistance/learns curse resistance abilities
Wimpy: has multiple weaknesses
Stoic: has numerous resistances/learns many resistance based abilities
Resourceful: learns abilities that improves post battle rewards
Pinch hitter: learns abilities that can be activated when in danger
Loyal: learns abilities that will be activated when allies are in danger
Zippy: speedy monster with abilities such as auto:haste or critical:haste
Rare: difficult to encounter or recruit

Source: https://www.gamefaqs.com/boards/619315-final-fantasy-xiii-2/61822400

Solution 3:

In addition to Adanion's answer the fourth attribute listed is just for fun. It has no in-game effect and is just meant to be cute or entertaining. Some of these are actually Cute, Zippy, and so on.

Only the first three attributes define the monster.