Use ships with phase missiles and research the tech that lets them penetrate shields/mitigation.  Assailants are your friends-but so are capitals.  It sounds like you've actually gotten the fleet composition done decently well-you just need to research the phase missile line.

Build more labs and do more research.  You should easily be able to fit a lab per planet (even if it's an asteroid), and unless you're going for RA, you don't need as many civilian labs as Vasari.

Definitely agree with Sole Soul. The phase missile line of research is critical to Vasari tactics, especially if you are fighting the Advent which are highly skilled in shield tech. Level 10 cap ships of the Advent can reach 84% shield mitigation, have only seen 74% with TEC and Vasari. The phase missiles can negate this.

20% damage or 20% penetration?

They go 10%/20% damage, 5%/10%/15%/20%/25%/30% penetration.  I don't remember exactly how many labs you'd need for that-though I'd guess it'd be more than three.

Incidentally, phase missiles are useful not only in that they can ignore mitigation (at the penetration rate, anyway), thereby doing much more damage, but also in that they can ignore shields (also at the penetration rate).  The key point here being that all you have destroy is the enemy's hull to destroy their ship-they can still have 500 or even 1000+ shields remaining when their ship goes boom.

I see.  So your primary issue was having no real "planets".  Even a volcanic would have helped you immensely.

I had 20% penatration i dont' think i had enough centers to upgrade damage. I agree with the no real planets part.

What are you talking about vasari have good resource economy TEC get credit and decent recource. Advent had about the weakest economy but their ships do more for lest cost. I say TEC and Vasari are balanced it's just that advent have 3 good ships that they spam. They don't need any mix of unit just a spam of these 3. (The carrier{even better than vasari one in hull and shields}, their lrm {huge damage and has lots of hull and shields more than vasari}, and their heavy assault cruiser {takes a pounding and doesn't die, even to vasari ship}) Tec and vasari need more of a mix to get up a decent fleet. Even the tec's best units can't match advent and vasari while some advent ships are easily a match for vasari. Vasari 1 on 1 ship class vs ship class will normally win but their ships are normally 10-30% more expensive and with the proper research on the other side you could sacrifice lets say 1 ship for an upgrade and win a battle. 10 lrm's vs 10 lrm's (area upgrade on one and bring the lrm's down to 9, they win).

Finally i continued playing the game and i lost the battle unfortunatly. But having my economy so much better and having stored a vast amount of resources (about 9000 credits, 2500 metal, 1500 crystal) I built up a new fleet again even stronger than before. I took out my friends defenses at his planet. I took pity on him and stopped attacking and warped to confront a huge ai fleet that took mine out. (caused decent casualties) After that we did some attacking and defending and i found an artifact called resiliant metaloids. The fighting continued but i'm pretty sure i got the game in the bag. I was able to take out an orange desert planet directly next to his terran world. I had to quit again with 2 fleets massing at a planet one jump away form my volcanic planet that i gained (you were right it did help). The volcanic planet had full tactical slots filled with 3 hangers 1 repairer 1 phase stabilizer and the rest in turrets. My main fleet had to leave the desert uncolonized to phase back to help defend cause there was no way even my full defenses could take out the fleet they had. When i do take out that fleet my eco will boost me to the top and i'll not take pity on my friend and wipe him out directly after.

P.S. thanks everyone for the help

Vasari ships are generally considered the toughest ships until upgrades are concerned. If you chose the Evacuator as your free capital (which is so common its almost unheard of to use a different one), hopefully, you've put ability points into Nano-Disassembler. Arguably, its the best anti-capital ability which inflicts an armor penalty of -2/-4/-6 on the target as well as dealing 30 hull damage per second (it ignores shields) for 20/30/40 seconds.

I do realize that you are short on logistics slots in this situation, however, if you can get a 4th Weapons Lab, research the Severun Overseer. These ships have an ability called Reactive Nanite Armor, which provides an instant boost of 250 hull (to both current and maximum hull) and 2 armor for one minute or until the additional hull points are depleted. In fact, if the one minute duration expires, the additional hull points remain even though the maximum hull points have returned to normal values and the armor bonus has expired (so on a ship with 700 max hull points, it can end up having 900 until it is damaged). Seeing that you already have a 20% shield negation on your phase missiles, you have at least 3 Weapons Labs. Tier 4 Military also opens up the Charged Missiles ability, which allows your Assilants to sacrifice mobility for extended range and an area of effect attack (it requires both the Assailant and Sentinel prototypes to be researched).

If I remember correctly, there is a possibility that Desert planets can be found in Centrifuge. If that's true, try to grab one of them. Fully upgraded, they have 36 logistics slots, which make it perfect for either a factory, research, or culture planet.

Also, take advantage of the fact that Advent players need at least 3 Hostility Temples to research Illuminators versus just 1 Weapons Lab for Vasari players for Assailants.

From what I've read and experienced, one point increase in armor is like a 5% increase in "effective" hull points, which also means that repair abilities are 5% more effective with the same increase. The first armor research subject is in Tier 3, the second armor subject in Tier 4, and research times for any subject is the same as any other subject in the same Tier (simply put, subjects in Tier X all have the same research time, X being any number between 1-8), so its no different than researching shield bypass for Phase Missiles.