You could say She tends to belittle people.
That is, to treat them as inferior or insignificant.
ell.stackexchange.com/users/10264/Tᴚoɯɐuo
I don't know an idiom that would express the sadistic pleasure of inflicting pain in others either physically or mentally, but there's a word borrowed from German.
Merriam-Webster Dictionary defines it as: schadenfreude: enjoyment obtained from the troubles of others; a feeling of enjoyment that comes from seeing or hearing about the troubles of other people.
EDIT:
However, Wikipedia describes an equivalent English expression: Roman holiday: metaphor from the poem Childe Harold's Pilgrimage by George Gordon, Lord Byron, where a gladiator in ancient Rome expects to be "butchered to make a Roman holiday" while the audience would take pleasure from watching his suffering.
The term suggests debauchery and disorder in addition to sadistic enjoyment.
ell.stackexchange.com/users/3223/Lucian Sava
You could say that person A often " puts people down ".
See definition 1(c) of "put down [phrasal verb]"
at the Merriam-Webster Learner's Dictionary entry for the verb put .
I am a native speaker of English, and I am familiar with the word "schadenfreude".
But I feel that, at least in English, "schadenfreude" carries no implication that there is communication between the people of any kind.
If person A heard that person B is in a tough situation and feels joy, that's probably "schadenfreude", but I don't think that's the situation kim123 is trying to describe.
ell.stackexchange.com/users/3673/Mark S.
I don't know of a word or phrase that captures everything you are describing.
I think to make himself feel good sounds fine.
So I recommend a few ways to change the first part of your sentence.
I provide this simplified model: Person A
_
_
__ Person B to make himself feel good.
Aside from the other good answers, I think bully (mentioned in the comments) and ridicule are also possible.
bully transitive verb 1 : to treat (someone) in a cruel, insulting, threatening, or aggressive fashion : to act like a bully toward &bullet; bullied her younger brother) (M-W)
ridicule : to laugh at and make jokes about (someone or something) in a cruel or harsh way : to make fun of (someone or something) (M-W) The context should imply that B would feel bad.
Crudely, you can say crap on (mildly offensive) or shit on (offensive): shit on somebody — phrasal verb with shit uk ​ /ʃɪt/
us ​ /ʃɪt/
verb present participle shitting, past tense and past participle shit, shat or shitted offensive to treat someone very badly and unkindly:
He made his money by shitting on other people.
(Cambridge Dictionary)
Lastly, you don't need it, but I think it's idiomatic to include just in the sentence.
It stresses the idea that Person A only does that to make himself feel good.
It makes A look really bad.
Person A
_
_
__ Person B just to make himself feel good.
ell.stackexchange.com/users/36187/Em.
I feel strongly that there is a phrase for this --
but I just can't think of it!
Eventually I stumbled upon something like building yourself up by tearing others down .
It returns quite a few search results (if not for that exact phrase, then several sub-phrases), but doesn't seem to be a direct quote of anyone in particular --
although I guess that's pretty much what idioms are.
ell.stackexchange.com/users/29165/pjs36
What I'm about to suggest is not an idiom or a phrase, but a very specific word which has the exact same meaning as the title.
Sadist
a person who gets pleasure, sometimes sexual, by being cruel to or hurting another person - Cambridge Dictionary
You can say that A is being sadistic towards B .
This word often has a negative sexual connotation associated with it, which is why I personally wouldn't recommend using it.
( By the way, I'm a little surprised that nobody even thought of it. )
ell.stackexchange.com/users/44797/Soha Farhin Pine
Bucket Dipper
There is a kids book, which I don't recall the name of.
In the book, all people are said to have imaginary happiness buckets.
The amount of happiness in it can get more or less.
Bucket fillers fill their buckets with happiness by being kind to others and in the process, fill others' buckets too.
Bucket dippers try to fill their own happiness buckets by dipping into others' happiness buckets (i.e. stealing their happiness by being mean and putting them down).
But they can never really get a bucket brimming with happiness; sometimes they just keep trying.
It's a useful observation about how some people work.
ell.stackexchange.com/users/55253/Chris
Your potential answer, "Feed ego at cost of others" does describe exactly what you want.
"Feed ego" is a positive term and "cost of others" is a negative.
The negative aspect affects the victim (the one being blamed) but the one doing the blaming will have a positive gain on their ego (thus feeding their ego).
Overall the effect is negative to an outside perspective but to the one trying to feel good the effect is a positive one or, in this case, they wouldn't be doing it.
ell.stackexchange.com/users/55225/Lee Curran
You are describing the most common, obvious form of verbal abuse.
Verbal abuse is a form of psychological abuse.
ell.stackexchange.com/users/55264/loopernow
Are there a stable expression for a situation when  Person A blames B and tells how B is bad in order to make himself (A) feel good ?  I would say something like "feed ego at cost of others", but I google it and it looks like "feed ego" has rather positive meaning in English and means "making feel good by doing good work or receiving a compliment".
Idiom for making others feel bad to make myself feel good?
ell.stackexchange.com
<idiom-request>
ell.stackexchange.com/questions/129291
ell.stackexchange.com/users/3252/klm123
Your suggestion of "Feed ego at cost of others" does describe exactly what you want.  The negative aspect affects the victim (the one being blamed) but the one doing the blaming will have a positive gain on their ego (thus feeding their ego). Feed ego at the expense of others is a good example of what you're looking for.
Feed ego at the expense of others is a good example of what you're looking for. The victim (the one who is being blamed) will suffer a negative effect, but the one who is blaming will benefit in terms of ego. Overall, the effect is negative from the outside, but it is positive for the person attempting to feel better, or they would not be doing it.