Go at your pace. If you want to go faster, then try that. But as you soon find out, if you submit your answer to Tactics Trainer in a very short amount of time, you may very well overlook something.
What are your goals in chess ? Do you want to be at your best level playing speed chess or playing standard or on-line chess ?
I've done hundreds of Tactics Trainer puzzles, but I'm still in the 700s zone. This is in large part because I like to take my time to analyze the board for each puzzle, and several have time limits around 30 seconds or less so I lose points for taking too long. However, when I do get a puzzle wrong, I take my time to figure out why it was the wrong move and what the correct move should be.
How long does it take other people to progress past this point? I've been going through the lessons as well... I decided to get back into this after a year's break, but I'm just curious if I'm missing something since I'm going so slow.