We had lots of adventures on our trip.
At first sight, I would translate 危ない目にあう as “I met dangerous eyes” which feels poetic, but I think it gives the idea. Digging a bit, 目にあう means to experience or go through something (negative).
So on the whole “We had a lot of adventures” seems like an understatement. “We had a lot of troubles” maybe?
Correct. The Japanese-English paid doesn’t match. 危ない目に遭う illustrates unpleasant seriously dangerous situations.
～目に遭う is a frequent idiom. You can find more example sentences on 英辞郎. We usually spell the idiom as 目に遭う in Kanji although 目にあう in Hiragana is also okay.
遭う（あう）in general means “to encounter (problematic/unfavorable situations etc.)”. 遭遇する（そうぐうする）is another expression.