Is there a way to be invincable on Megaman battle network 3 blue

Not quite. Using barrier chips prevents damage, and using a 500Barrier program advance in conjunction with a Sanctuary gives you 1000 extra HP. Invis will hide you from most enemies (notably NOT the Killereye family), mole will help hide you between attacks, shadow will hide you from everything except for swords. Auras make you invincible to varying amounts of damage (100, 200, 300 at a time) but eventually wear off. The only remaining option is to obtain a grass style with a grass stage and undershirt. That way, no hit on you (unless you only have one hp) will kill you, and you'll constantly regenerate life from the grass stage. Don't use this when fighting a fire enemy, for obvious reasons.