How do I know If my wolves are battle wolves?

Battle CP is directly related to how much damage your wolf deal. Having filled that attribute allows the wolf to deal the most damage.

Battle experience: Your wolf can gain extra damage bonus if they reach a certain amount of battle experience.

A wolf with 200/200 battle who has 0 battle experience, will deal a "max basic damage" of 23 HP.

Reaching the "Slashing Bite" (275BE) and "Neck Snap" (525BE) moves will give each, a +2 extra damage bonus . Appling those to the "max basic damage" it will be 25 HP damage for a wolf with 275BE (useful to defeat a wolf in four hits instead of five in a PvP battle), and 27HP damage for a wolf with 525BE or more.

The ultimate battle move a wolf can learn is "Death Grip" (925BE),

this leads to have the max chance of hitting critically (a critical hit makes your wolf deal a +15 extra damage in explore and +10 damage in PvP). Most battle packs want to train their wolves to that point. If a death grip wolf doesn't hit a NPC it will be because they avoided the hit and not because your wolf "misses".

Resolve is useful for accuracy, your wolf will miss less hits.

Agility is useful for evasion, your wolf will dodge more hits from enemies.

Battle boost: best is at the top.

-Divine health: your wolf have 150 HP instead of 100HP.

-Elite Speed: allows a max battle of 250HP. Makes your wolf deal the same damage as a death grip wolf without needing to train them. Chance of hitting twice

-Crushing Strenght: allows a max battle of 250HP. Makes your wolf deal the same damage as a death grip wolf without needing to train them.

-Nimble Foot: allows a max agility of 250HP.

-Unparalell Learning: allows a max resolve of 250HP, chance of getting 2BE instead of 1BE per kill. This chance is aproximately 5%.

Weight:
Weight matters for explore, but does not for PvP. People tend to look for 130+lb wolves as known as "heavyweight"

Weight bonus is applied for the "basic max damage" which is 23 for a nontrained wolf.

Weight	Bonus
75lb ~ 89 lb	-5 damage, +5 agility
90lb ~ 109 lb	-2 damage, +2 agility
110lb ~ 129 lb	+2 damage, -2 agility
130lb ~ 150 lb	+5 damage, -5 agility

Vitals: a wolf will get a damage bonus/penalty depending of which values they have in their vitals, when a natural event is occurring (Flood, Earthquake, Hurricane, Blizzard).

Having all these values positive is the most ideal situation.

Again, this only affects explore and not PvP. And the event that you'll see more often is Blizzard.
Vitals won't give more than a +5 damage bonus