Are there actual levels in Tiger! Tiger! aside of first one?

I've managed to beat level 1 of Tiger! Tiger! minigame several times. getting some equipment for Poppi. Yet, game doesn't allow me to continue to level 2, and just ends. So, my actual question is - are there more levels? If so, are there any conditions to unlock them (if it is plot-related - please, don't spoil it, just say "it's plot-related")?

Yes

Once you continue in the main story, new levels will open up.

• Level 2 will open up when you enter Uraya.

• Level 3 will open up when you enter Mor Ardain

• Level 4 will open up when you enter Tantal

• Level 5 will open up when you enter the World Tree