I just played a solo game. Here and there reads it is only complete when you teleport through 2 telegates in the same turn. It is hard enough to teleport through 1 and it seems completely luck based to draw an encounter to place a 3rd gate. Help me if I am missing something because I feel this challenge is near impossible.

This challenge can be quite difficult, if you are not the centaur type race which has abilities to assist in telegating. Also there is a jump gate card which allows you to gate to a telegate. This challenge is difficult but not impossible. The ideal way to do it is to use a Hard Burn with a level 3 pilot increasing your speed or a throttle booster. If you're playing with intel the star maps will come in handy. It involves entering one telegate with a navigation die guaranteeing your teleport, then having enough movement to return to the other telegate.