I was very frustrated with this matchup as unless I was in rush position I found it a very tough nut to crack. The key seems to be unit micro, which is pretty foreign for most TEC eco players. Just a few tips on winning large engagements (titan, 3-4 caps, 50+ bombers and 100+ frigates with support cruisers). You need mid-level caps for this, so either wait until you have the credits to buy levels to attack or delay truce among rogues and creep a bit.
Against advent carrier spam you need 2 level 3 Koi casting flak (buy the 2 levels, manual cast at beginning). Robots near them to repair and that way the hoshikos don't die. A bit of flak to help mop up is nice if you have the fleet space.
Dunov's EMP (ideally level 3 ship with level 2 EMP at least) is very synergistic with the Ragnarov titan's great snipe ability: pick a cap in the middle of the battleball, snipe, EMP then snipe again. If you have upgraded cielos then you can designate target as well if you want. Cap should be dead and all of the stuff around it will have no shields. Follow with scattershot to kill much of the battleball outright (including guardians after which repulse is no longer an issue) and leave the rest with no shields, no AM (for caps and carriers) and no armor. A skilled advent will run his cap out of formation after first snipe, but akkan's ion bolt can lock it down. The cherry here is that doing this a couple times levels your titan very quickly, and once it get ultimate ability this becomes even deadlier. Ideal if you can catch him trying to get a malice combo off. If you mess it up, have akkan cast armistice and run.
Send corvettes/cobalts at his carriers at the edge of the grav well if he chooses to keep them there.
LRFs don't really work against advent unless he is spamming disciples and/or illums. Kodiaks and flak do work if you can keep hoshikos alive (dunov and more flak) but take a while to get the job done. However, upgrade missile damage anyway as it is the path to novas and helps your bombers.
Xenophobia tech really helps deal with Advent natural culture push.