Hapan battle dragons are the mainstay of the Hapan consortium and these ships are not to be overlooked. They have a high rate of fire and have no targetable hardpoints. Additionally, they are usually deployed en masse and can overwhelm shields with copius amounts of fire. Additionally, My'til fighters proveide an excellent fighter screen to intercept bombers.

Beta and Nova cruisers are corvettes and frigates respectively, and are nowhere as dangerous as battle dragons. However, Nova cruisers carry a larger compliment of fighters than battle dragons and have a longer effective range. Beta cruisers further screen ships against fighter attack.

Battle dragons have a high rate of fire and relatively low accuracy, which they make up for in numbers. While spamming fighters work, it can be hard on the graphics as well as galactic credit pool. Using a smaller fleet of large ships works, but must be positioned carefully. Attacking from multiple angles divides the firepower of battledragons and attacking from a range further improves this. Weapons that have a lower rate of fire but higher damage i.e. proton torpedo launchers work magic. Victory 1 & 2s, bothan crusiers, and EotH Peltast destroyers. They combine range and firepower. Additionally since battledragons have no hardpoints, they can be fired at and waste less shots.
After some planning and experimenting, a pincer/trident maneuver is optimal. Since battle dragons can only fire in a forward arc, flanking is essential. First, drop in a larger ship that can absorb fire pretty well. The AI will recognize this and prioritize it due to proximity. Wait for the dragons to bunch up and make their way to the first fleet. When they are bunched up, Deploy another fleet behind and to the side of them, but be sure to maintain range. This effectively will divide the fleet firepower to 1/3 per fleet. Ensure to boost weapon power as early as possible and destroy as many at a range as possible. When they close the gap and start firing, boost shield power to soak up damage while your squishier ships take potshots.
Losses should be light, and pretty soon you should have control of Hapan space. EotH is the best suited to deal with hapans due to Rhokea frigates wich hace incredible range and damage, and peltasts also have range and stopping power as well. Additionally, the low profile makes Rhokeas hard to hit due to the spread of the shots.