Hi Jpara, just got back from KL yesterday.  I tried to visit a few tackle shops but they were all closed due to the new year break or the fact it was Sunday so I can't vouch for range or prices.

 

The post above is a bit out of date (Sabre tackle has moved) but below is what I figured out while I was there:

 

Sabre Tackle is here (best to catch a taxi now): https://www.google.com.au/maps/place/Sabre+Tackle+(M)+Sdn.+Bhd./@3.1298242,101.7068522,15.75z/data=!4m5!1m2!2m1!1ssabre+tackle!3m1!1s0x31cc36202379c40f:0x3662ec4e68df2278

 

Great Ono Sportfishing is here (short walk if you are staying on Bukit Bintang or from the monorail station): https://www.google.com.au/maps/place/13,+Jalan+Barat,+Pudu,+55100+Kuala+Lumpur,+Wilayah+Persekutuan+Kuala+Lumpur,+Malaysia/@3.1451754,101.7148845,19z/data=!3m1!4b1!4m2!3m1!1s0x31cc362e60233327:0x7ec5841431be58c7

 

There is also the following places but I didn't make it out to any of them:

 

TCE Tackles: https://www.google.com.au/maps/place/Tce+Tackles+Sdn.+Bhd./@3.1303964,101.7291089,17z/data=!4m7!1m4!3m3!1s0x31cc366a97d24201:0xf7db9ff1f03116cf!2s241,+Jalan+Mahkota,+Maluri,+55100+Kuala+Lumpur,+Wilayah+Persekutuan+Kuala+Lumpur,+Malaysia!3b1!3m1!1s0x31cc366a949436fd:0x1d9a70b94e41d4df

 

Young Trading (looks close to Pudu train station): https://www.google.com.au/maps/place/Young+Trading+Store/@3.13311,101.7126415,18z/data=!4m5!1m2!2m1!1sfishing+tackle!3m1!1s0x0000000000000000:0x7a1ba26a5817a784

 

Fish Tail (close to the central market): https://www.google.com.au/maps/place/Fish+Tail+Sdn.+Bhd./@3.1476195,101.6955237,19.25z/data=!4m5!1m2!2m1!1sfishing+tackle!3m1!1s0x0000000000000000:0xf97e6d783eb986b4

 

My advice would be to call first if you can to make sure they are open as the hours you can find online seem to be a bit fluid.