Advent can use Illuminators and Guardians (without Repulsion) to surprising effect against Heavy Cruisers if backed up by a Progenitor Mothership. They still need to outnumber the Heavy Cruisers, but the Heavy Cruisers are in a tough spot to focus fire on the Mothership to stop Shield Regeneration and Malice, the Guardians to stop protecting the Mothership and Illuminators, or the Illuminators, who will be tearing into the Heavy Cruisers.

Repulsion is T5 Military, so I'm guessing that's not the kind of counter you would like , being the same tier as Heavy Cruisers, but if you use it with Illumintors the Heavy Cruisers will usually cry and die, since they lack the range to combat that.

Bombers can work, but they usually take a while to work their magic, and are fairly cheaply countered by Flak, so a dangerous choice.

Usually, if your opponent rushes Heavy Cruisers and you haven't done substantial damage to them with LRMs, you are in trouble unless you can tech to match it.

As advent you better have repulsion or HC's of your own if your opponent drops a bunch of enforcers or kodiaks on you. However, you should be able to get 3 or so guardians with repulsion by the time your opponent has heavy cruisers so it really should be a non issue.

if you are vassari then you better have HC's as well. It's like any other game. If you ignore your opponent and pursue a bunch of econ stuff while ignoring your own army then don't be surprised if a bunch of high tech units blow you away. If someone really really is HC rushing then a small group of frigates can blow them away before they get any. Putting pressure on your opponent throughout the course of the game insures that they can't out tech you and at the same time makes sure that they are unable to build up secret fleets that you don't know about.

Like every other RTS game ever made you can't sit back and expect an easy answer if you made the blatant mistakes of ignoring your enemy, ignoring your own army, and ignoring your military research. At the very least you should have been scouting your enemy and noticing the lack of a large fleet while at the same time noticing a suspicious number of military labs. Take your scouts off of auto-explore and instead have them make circling runs through enemy planets. If you notice a bunch of military labs and a weak army go blow up some labs. Every race needs 5 labs in order to even build a HC.