How do you know when the next tier is coming up?

Like, my pet is at tier 6 now, and I'm working at getting all it's battle stats to 700. Would my pet be at tier 7 when I get all the stats to 700?

http://subeta.net/forums/view/861678

This topic should help.

The Ultimate Battle Guide

The best way is to follow this battling guide. And no, tier 7 is 3400 total stats or around 850 / stat.

Whoa;; All right, thank you!

The jump between tiers increases pretty high as you progress to higher tiers. When you reach a new tier it becomes much harder to level up since training times/costs increase as well as the cost of stats using EXP in the Battle Coliseum.