Practicing my Japanese - someone who is a native speaker should translate this because stuff like わけ is … sometimes hard to directly translate without years of experience. But, here’s what I got:
 
Panel 1:  
Fluttershy:  
えいっ  
(yells)
 
べちっ  
(ba-te - sound effect of hitting)
 
Rainbow Dash:  
ょゎっちぃな~  
Youchies, right?  
も っと強く  
Harder!  
できなぃわけ?  
Can’t you? Or is that it?
 
Panel 2:  
Rarity:  
ぁなた遣  
Hand it over, you.  
何ゃってるのょ.  
What’ya doing?
 
(non-dialog 引くわよ - getting pulled into an argument?)  
(non-dialog AJのは死ねけど - “I will die for AJ” - wot?)
 
Rainbow Dash:  
キミらみたいな  
I like how you lame  
文化系女子 の  
culture-based girls  
バンチなんか  
are a soft bunch.  
効かないって  
you can’t stand up to  
テスト！  
the test!
 
Panel 3:  
Rarity:  
そうねえ•••  
Geez …  
一回ゃってみても  
I’ll try ya  
ぃぃかしら?  
If it’s ok, ya know?
 
(heart beat sound effects)
 
Rainbow:  
はいはい  
Sure, sure  
どうぞ  
Go ahead.
 
つてさようと  
Ya know, this could be painful …  
待って  
Wait  
なんでそんな気合入って  
(why would she) say such a thing?
 
(ドボオ - sound effect of punch to the stomach)
 
Or, transliterating, something like:
 
Fluttershy: KIAAAAA! (failed punch)
 
Rainbow Dash: Wow. Harder! Is that all you’ve got?
 
Rarity: Hold on you two. What are you doing?
 
Rainbow Dash: Just enjoying how you lame culture-based girls are such a soft bunch. You can’t stand up to the test!
 
Rarity: Geez. Ok, I’ll give it a try. HERE IT COMES!
 
Rainbow Dash: Yeah, yeah - go ahead.
 
Rainbow Dash: Wait … that yell? Is she serious? This could hurt …
 
I hope someone who is a native speaker will correct my attempt.

Rarity being an expert at CQC is a bit of a meme on the japan side of the fandom.

whoa!  
I’ve think she’ve take it too far…

I assume the joke is that Rarity is unexpectedly a super beefy martial artist.