For me actually playing with vasari is easiest way to win hard ai even 2 of them ( 3 teamed allied to kill depends much on map you are playing on. U need good planets near you and only one choke point. 4 is impossible without ally on your side. That means human ally and double sb on choke points. Again it depends on the map u are paying.)
For instance they got movable sb which can reduce frontal attack and they gave phase missiles which enable you that u don't have to deal with ships shields especially if u go against guardians. True they have nothing for buildings to kill really quick but they have very strong bombers which if u have enough of them they are good enough (again with phase). They also have overseers who with some AM research 10 of them can heal your sb indefinitely if u don,t get hit by 20 ogrows or so and if u have air cover.
PS It might be easier at start of if u get 2 hard ai's with teams locked since they will throw some of their fleet at each other.
Here is how i play against 2 allied hard ai as vas. Other races are similar you just need to incorporate races strength in what u are building.
First i build carrier with fighters on them and then build sb on choke point planet where he's going to attack. U need to be really quick if u go against 2 of them) I don't expand too much. Buy some upgrades on my sb and build another carrier with repair ability, build repair around sb it and some cannons with reintegration disabled ability. While ai's attack I keep lvl up my caps (repair and fighter ability which consumes no am) and do overseer, am, armor, hull and phase research. Build 10 overseers to heal your sb as soon as possible. Don't forget to keep retreating your caps near out if damaged and repair them. When my research is done i build another 2 kortuls caps or another 2 cariers depends what fleet ai are attacking with lvl them and up as well atleast to lvl 6.
As vas it's good to have resource collection by your cap option so be sure u research this and cheaper ships option.
After all this is done my 4 caps should be lvl 10 all so now i build fleet of mine layers some assailants and carrier frigates if you can get 7 military labs go 4 subverters. I don't go 4 heavies because if u don't have enough of them they are useless (that is 20+). U need bombers now so switch ur caps and carriers on bombers but leave 10 fighters in ur ships hangars especially if ai has mass flak. Let them out when they are down to 5 or less. When I attack i stay near gravity well edge lay mines between his fleet build sb and when sb build and some upgrades on it i go kill his structures and sb which are definitely build. Keep building overseers u should have 20 by now. And keep researching military tree. I go 1 planet at the time now. Kill planet build some trade next one ..... etc.
You got upper hand by now and game can drag out for a while since vasari are terrible against buildings and almost 4 sure u need sb to counter AI s better income research and faster building ship speed. So u need a lot of bombers if you are going to try without sb. But in the end you will need one to defend when you move on to next planet
If you Play as tec its harder since your sb is sort of useless or not so good. TEC sb is really good online since opponent never knows if you have Red Button on it. AI just rebuilds too fast so RB doesn't work there. Make sure u build plenty of hoshikas with disable weapons on them and repair around ur sb especiall if u go against tec or advent since they got building destroyers.
Advent is much easier with their spin and meteor on their sb + you can build culture on it and lvl 3 culture upgrade is really strong. But as advent u need to get some ilum spam soon otherwise ur sb will die and some guardians with repulse to push ai's fleet to yous sb.
PPS Not sure how it works against 1 hard ai but against 2 building fleet too soon is waste of money since it will definitely die.