Dangerous looking bookshelf

So we are in the middle of moving house, we are still sleeping in the old house and living there but we have moved some new furniture into the new place. We have a book shelf there that is a bit wobbly and i can see Samson climbing up it... and "splat". Im worrying myself sick about it and he isnt even there yet. lol. Not sure what to do about it. We would be renting the property and im not sure what the landlords opinion of new screws in the wall would be, but if its the only wise solution i might just do it and claim they were there before i moved it. Tie the shelfs to the wall that way. Has anyone got any other suggestions to discourage Samson from leaping about dangerous furniture.

My daughter is in an apt that forbids holes in the wall. That is not reasonable, so we will fill them when she leaves.

She has a tall bookshelf that we have attached to the wall with an "L" bracket. It is holding up well at this point.

yeah, i would just fill the holes when you leave, that's what we're planning to do though they're fine with us making holes and even painting the place. we just want all of our deposit back.

Or just plain ask the landlord about securing it better (and offer to pay for the job).