There are a couple ways to complete this fairly easily.
If you've completed longshot, you will get a bunch of players from that mode to use on your MUT. If you press Y on your roster and choose generate best lineup, you can set "Longshot" as one of your chemistries.
For the other chemistry, go into your item book and sort by team. Whichever team you currently have the most players for, go to the auction house and buy cheap players from that team until you have 5 of different positions. Then start those 5.
For example, I already had 2 Giants players on my squad from the get go, so I found 3 super cheap Giant's players in the auction house. I then activated both the Longshot and Giants chemistries and the achievement popped.
I would choose OL/DL players for the cards you purchase because none of the Longshot players play on the lines.