You can't request a trade in your first Be A Pro season. The coach will basically tell you that a washing machine is worth more than your trade value. So after you play through a season to get some of the other trophies, sign a new contract (preferably the smallest cap hit so you are easier to trade) and simulate to the start of the regular season. You can now request a trade. You will still need to play some games to keep your point production up. I had to make it almost halfway through the season before I finally got traded. The first time I got traded, the achievement didn't unlock so I tried again and it still didn't unlock. I had to start a new Be A Pro, and get traded on that save for the achievement to finally unlock. And if you get demoted to the AHL, then get traded, it doesn't unlock either and that could be one of the causes for the achievement being glitchy.
If the achievement seems glitched, start a brand new Be A Pro career and DO NOT request a trade until the 2nd regular season has started. The achievement should unlock properly now.