So recently my bath tub has been slowly draining and its getting worse and worse which its bound to get clogged. The problem is that the landlord won't fix it unless it's the Main pipeline. Our landlord said its our problem to fixs our clogs. What are my right? And isn't his responsibility to fix it regardless?

I'm not sure because it depends on the laws in your area, but in my area it was not the landlords responsibility. Drain-O is not very expensive and it may help.

NO, it's not his responsibility to get your hair out of the drain. I agree with LHolly... go get some Draino or use a plunger on the drain opening

Are you living in an apartment or a home? What are the terms of the lease agreement? Simple things like pouring drain-o down the drain should be the first step you take. If that does not solve the problem, then contact your landlord. A plumber might need to be called. If you have to pay for that or if the landlord does, that should be covered in your lease. Just a note, even if this happens to be your landlord's responsibility and he does call the plumber - if the plumber finds something that you could have prevented - then you could be liable for payment.

So recently my bath tub has been slowly draining and its getting worse and worse which its bound to get clogged. The problem is that the landlord won't fix it unless its the Main pipeline. our landlord said its our problem to fixs our clogs. What are my right? and isn't his responsibility to fix it regardless?
The drain worked when you moved in and your hair clogged it up. It's on you to clear it up. We cam walk you through snaking the tub drain if you wish. Your choice! Regards, Tom

How do we know it is hair causing the problem? Is that a safe assumption?

Your rights are spelled out in your contract. Does your contract with the owner/ lease agent tell you that you are responsible for interior maintenance? As for tub drains that are slow, the most common is hair, the next most common is adjustment. Is your tub drain the type you actuate it with a lever or some other way on the overflow or do you actuate it at the drain itself? As a rule, I never suggest drano or other chemicals. In the 34 years I have been doing plumbing I have never used drano and only once used a chemical on a slow drain other than a urinal. On a urinal I use a strong chemical to clear the urinary salt in the bowl and the drain, and some times that does not work. You will find that chemicals will harm the finish on the tub trim.
You are likely to find hair in the cross on the drain. Make a little hook using a coat hanger about 8" long. bend a handle on one end and a 1/2" L on the other. Simply grab the hair with the hook and pull out. Hair clogs are typically never in the trap and that is where you chemical will go.

How do we know it is hair causing the problem? Is that a safe assumption?
Hair matted with soap scum is the major cause of tub/shower and lavatory clogs, however, it doesn't make any difference what clogged the drain, it's the tenants responsibility to do minor maintenance on the rental unit. The tenant caused it and he should clear it. Regards, Tom