The Parallel Universe (PU) is a secret safari location which is unlocked after you win 50 battles in each of the other 7 safari locations. Traveling to PU costs 5x the regular travel cost. It is a special safari because here any critter can appear and can appear with any appendage (unlike the other locations). This makes PU the ultimate place to find critter samples.
Critters found in PU have a minimum level of 20, regardless of the level or tier of the critter you go there with; all critters found under red boss tiles equal or exceed the tier of your current critter.
Something to note is that higher tiers in Parallel Universe can be below the usual level in other places. (A level 33 owlbear, for example.) Each tier of critter has a min level when one chooses a red dragon square. The square is minimally the tier of the critter with you (e.g. A wyrm getting the square will get a resulting wyrm, cerberus, or beholder.)
The minimum levels are as follows:
Tier 1- Level 20
Tier 2-Level 30
Tier 3-Level 40
Tier 4- Level 65
Tier 5- Level 105
Currently the game does not display your victory counts in each location. So, many players recommend recording your victories somewhere so you can unlock PU as fast as possible. Then the game needs to be refreshed to unlock. This is the best place to find creatures. Your best bet is to level up to get there. If you want a dragon, go here.