So, I've looked over the trailer and gathered some info.
The large enemy at the beginning is called "Anficoerias".
The neckless lizard dog enemies are called "Wild Lupus".
The large grasshopper is called "Akushoku no Kasuparu" (Evil Eater Casper? Unique monster)
The two spiders are called "Jorougumo Doukutsu" (Yellow Spider Cave; yes, that's the monsters name)
The large robot enemy is called "Vasara".
The enemy with lots of eyes is "Tekken no Bruno" (Iron Fist Bruno)
The enemy that can't be seen well is calld "Sleipnir Mira"
"Cooperation" attack (party attack) uses up 100 units of the gauge and causes "cooperation" effect.
"Braveheart" increases targets fighting accuracy, attack power and wave damage.
"Rage" attack reduces the targets fighting attack power
"Rising" increases damage dealt to an enemy that's targeting you.
"Missile" shoots concentrated missiles at the enemy.
"Grenade" causes a "sweltering heat" effect and hits 1 enemy.
"Bluse Blast" causes break status, and hits enemies in a straight line.
"Advance" increases your AT damage and heals your HP over time; used on yourself.
"Heavy Bomber" hauses "heat" status and affects a circular area around you after jumping foreward
"Sword Wind" attacks enemies around you with a blade of wind.
The Dolls "Beam Saber 1" attack causes "Physical Defence Down"
The Doll attack that cuts off Anficoerias' head in one go is called "Anti-matter Bastard (Close attack)". Close refers to distance from enemy. It does major damage.
When "Tester" gets killed the second enemy behind does too, dropping "(Temporary) Treasure Box Name"
The Doll is called "Mass-production Model Doll".
When in motorcycle mode he picks up a blue orb containing a "Kebo Carrot" (Kebo may refer the the areas name?)