Compound Techs use two elements in their attacks. They’re available from the photon shop for a low price of 50 photon spheres. You equip these on your sub palette as a Force or Techer and charge them by hitting enemies with regular Techs. After the charge is finished, you can choose one of these to cast. Casting a Compound Tech will use up the charge, but their cooldowns are independent. These are one of your major sources of damage so don’t make these go to waste!
So because these use two elements, you should prioritize using the one that matches the elements you chose for your skill tree. If nothing matches, you did something horribly wrong in your skill planning. The combinations are ice+light, fire+dark, and lightning+wind.

Barantsion (Ice and Light)
Create two blades of ice and then dash forward to slash up your enemies. You can easily get hit out of the dash. A common trick is to use the ring that gives you Massive Hunter to give yourself super armor before casting. Honestly the range on this isn’t very large. It might take a few tries to get used to the dashing part. I know I missed a couple times by zooming right past my target. =(

Fomelgion (Fire and Dark)
Fire a laser continuously for a few seconds. Be careful because you have super armor throughout this move and can get hit multiple times. I like this compound Tech the best. You can control where you want to move the laser around in third person mode. The range is pretty big too so this can take down mobs really quick. The burn rate is incredibly high as well.

Zandion (Lightning and Wind)
Dash around creating lightning bolts around you before finishing with a hurricane. There is invulnerability throughout the flight until the finish. I know this compound Tech can do decent damage and kill mobs, but I can never aim it right. The best way I’ve found is to lock onto where you want to target and input your directions like you’re moving sideways. This makes you do tight spins around the locked area. The lightning starts the moment you start moving so start close to the enemy to make use of every hit.
Simple Compound Techs
Simple Compound Techs can be unlocked by completing a client order from Marlu where you kill demons and complete the Enchanted Forest free field. Equip these to your weapon like you can with a regular Tech. Unlike regular Compound Techs, these don’t require charging a bar. Instead, they take up a comparatively large amount of PP. Right now (Fall 2018), they cost way too much PP for what they do. Maybe if there is a rebalance they would be more useful. (Pictures maybe when I stop being lazy)
Re Barantsia (Ice and Light)
Fly around with wings of ice while shooting projectiles. Ending this will cause a light explosion around you. Hold down the Tech button to keep flying. The flight consumes PP continuously. The speed and damage are really lack luster compared to Sa Foie Type-Zero or Ilzonde. Not recommended.
Re Fomelgia (Fire and Dark)
Dash across the ground with a flaming spear. Ending this will throw out a cone of fire spears. Hold down the Tech button to keep moving. The movement uses PP continuously and the ender throws you backwards a bit. The PP cost compared to the distance traveled is very inefficient. Just use Sa Foie Type-Zero instead.
Re Zandia (Lightning and Wind)
Summon a tornado that vacuums in nearby enemies and then shoots down lightning at its center. Hold down the Tech button to aim, then let go to cast the tornado. You can extend the duration of the tornado for the cost of more PP by repeatedly pressing the Tech button. If you have the PP generating means, this is actually a good replacement for Zondeel when mobbing. This is probably the only one I would recommend being usable for certain situations.
