Your build is all wrong for dealing with him.
or
and
are basically musts.
since you dont really need to push against nasus (thats what he wants you to do)
>
if one cleanse is enough to kill him taking
can be an ok way to deal with constant withering. Honestly though once he has maxed cdr and wither unless you are way ahead you shouldnt really be the one to go after him as tryndamere dosent really have anything to deal with tanks like other melee caries.
you can try try to use w to mess up him qing the cannon minions.
killing his tower early generally isnt the way to go. freezing the wave and standing on his side of it and zoning him is your goal. rather than pushing to his tower and wailing on it you are trying to maximize the number of minions his tower takes. when you kill him you can shove to tower and kill minions if there and if not go aggressively ward their jungle to steal camps and even try to kill their jungler.
Tryndamere is strong at taking objectives. push to take baron rift herald and even dragons(harder because of distance. tp helps though if you need to get back to save tower)
the second his tower goes down the time bomb starts he now only has to worry about his minions taking stacks from him and he can push out super slowly and quickly gain stacks. just like tryndamere you cant keep nasus down forever. this is where normally as a top player youd be trying to snowball your other laners and force teamfights you should win because you are ahead by beating up on nasus in his weak early game. The problem is tryndameres teamfighting sucks.
you are also dont need ignite. you can easily smoke him early take tp to make plays/stop nasus split push or exhaust to help out in teamfights.
The other way you can play is a base race. Take tp. Pressure early and destroy top towers until people start rotating and teamfigts start breaking out. at that point you can go bot and try to out shove him.
are decent items as you are looking for dueling potential and fast push. you should take 2 people at least to kill you, which would leave your team in a 4v2.
takes alot more of your team playing well around what you are doing and taking advantages of mismatches you are creating.
since you are letting nasus basically free stack you have a small window before he gets rolling, and in that window you need to probably get an inhib in one of the other 2 lanes or you shot yourself in the foot for no reason.
No great way to handle it.