Help with DIY wall fix

Hello!
I'm having an issue with my landlord. Long story short..I made a mistake of not taking a picture of the crack by the walls when I moved in. Now I have to move out and she's trying to keep compensation for the said crack. So im just trying to keep my deposit.
Anyway.. is there a fix to this wall I can do by myself?
Note: it took out the flaky wall plaster/paint so you can get a better idea.

Please let me know how I can fix it and what all do I need from the hardware store.
Any help is appreciated! Thank you in advance.