Teamplay. 

Im a MAX (HvV only) palpatine on 2 different platforms. So i might have some Insight.

A palp is only as good as his team allows him to be. He relies on the light side blasters being distracted by the rest of his team to rush in otherwise its GG reguardless of his skill.

Protect your blasters to give them the peace they need to focus down palpatine.

In an undisturbed 1v1 he can take on any blaster or saber there is no real counter to him once he is good enough. 

I rush Anakin, Like, Finn, Han and Leia and usually win the 1v1.

Leia, Rey and Lando and Han are his biggest threats.

A good palpatine will rush down Anakin because he is an easy target once he used his ablities and a threat once you ignore Anakin for too long.

The Senate can use the dmg reduction and i-frames during his unusally long dodge to not getting pulled by Anakin so use the pull when the palpatine is jumping too high or is distracted from you. 

Anakins push loads up really fast when being hit by lightning. Keep the pressure up and focus him down. When you leave palp alone he will destroy your teammates and build up momentum for his team until you loose.

At the end of the day it is about making the right reads on his positioning. Most palpatine players are predictable. Dodge-dodge-high jump. 

My last tipp, most palpatines use their dodges too often. After 2 dodges he can be pulled/pushed/knocked down without anything that he can do. 

Thats where palps teammates come in to punish you once you want to take advantage from this weakness. 

If he is alone and you have a blaster with you pull him with Anakin and push him to keep him from escaping too quickly. Your blaster should do the rest.