
猫をかぶる
to feign friendliness or innocence; to play the hypocrite; to be a wolf in sheep's clothing
Literally, this means, "to wear a cat on the head."
かぶる normally means, "to wear hats," "to put on a hat," or "to put on clothes such as a sweater or a pullover (which needs to be pulled over one's head)." But it is also used to be "covered with" things like dust or snow or water over the head.
The idiom means to pretend to be nice when you really aren't while hiding one's intentions or true personality in order to be liked by others intentionally or unintentionally.

The small sentence to the right of the cat says,
頭、あったか~い。
atama, attakai.
(My) head is so warm.
- 頭 head
- あったか~い warm; nice and warm [a very casual variation of あたたかい]
The bottom sentence says,
あたし、猫なんてかぶってないよ。
I'm not "wearing a cat" or anything.
atashi, neko nante kabutte nai yo.
- あたし I [a feminine first person pronoun; very casual compared to わたし]
- 猫 cat
- なんて such things like; such a thing like [a casual variation (version?) of など (such as; etc.) and has a nuance of dismissing or putting down what precedes it (猫); なんて is also used to add a sense of surprise to the preceding word depending on the context]
- •かぶってない is not wearing [かぶってない is a casual contracted variation of かぶっていない (~ていない→~てない); (~て)いない (not ~ing). It is a negative continuous form of (~て)いる which indicates a continual state or condition; likewise, かぶってる is a casual contracted variation of かぶっている (is wearing)]
- よ (casual ender for emphasis)
猫をかぶっていても、あなたの正体はばれています。
neko o kabutte itemo, anata no shoutai wa barete imasu.
Even if you hide it by pretending to be nice, your true color is already known.
- いても even if (you hide your true self) [いて te-form of いる (a part of かぶっている); も (even); “te-from verb + も” is “even if doing ~”]
- あなたの your
- 正体 true character; true form [正 (right; correct)+ 体 (body)]
- ばれています is revealed (already); is (already) been exposed; is (already) known [from ばれる (to be revealed; to be exposed); ばれて (te-form of ばれる); います from いる (continuous form indicating a state (“being revealed”; “being known”)]
彼女は、本当はおてんばなのに、好きな男の子の前では、猫をかぶっています。
kanojo wa, hontou wa otenba nanoni, suki na otoko no ko no mae dewa, neko o kabutte imasu.
She's really a tomboy, but when around the boy she likes, she plays it sweet.
- 彼女 she
- 本当は in reality; actually; in actuality [本当 (reality; truth; fact)]
- おてんば tomboy
- なのに although; but [“noun/ na-adjective + なのに”;”verb / i-adjective + のに”]
- 好きな (the boy she) likes
- 男の子 boy; male
- の前で in front of