I just had my first successful game (on easy though, so it will probably be much harder on the other difficulties). A few things I did (it was a very short game!):
- start off with a lot of hunt pirate convoy missions for the bribe items. these items are very useful; with some races you can raise your influence directly, with others you get discounts etc. ESSENTIAL. Also, they dont cost a lot of time. Ideally, you "rescue" some of the pirates which you can then sell or give back to their people for free (i guess you could sell them as slaves but I did not do that)
- START TRADE ROUTES. Cannot emphasize this enough. If you can get a trade route going between two races, they will LOVE each other after a few years. I got several of these started very early. You can even get trade routes with not-yet-spacefaring nations, which I found a bit strange.
- Look if you can give spacefaring to some races without pissing the existing ones off too much. Consider doing quests.
- I started my federation with the Andor and Skylaxians. I very quckly got the Acutians to join, since they loved both the Andor and the Skylaxians (thank you trade routes!).
- The Acutians went and built a competent fleet. They proceeded to attack ALL the non-federation races one-by-one except the Burlusts, who were not spacefaring. I convinced them to stop attacking, which gave me lots of influence with the "victims" -> I could eventually invite the Thoraxians and the Evuck. The Peltians were convinced by the Skylaxians (I think?) to join. They hated me, but liked the Skyaxians, so that was fine.
- the third attack of the Acutians were against the pig people. Unfortunately I did not have enough credits to make them back off, so the Acutians took their planet.
- I then fulfilled a quest for the Burlust, to make them spacefaring. I could immediately get them to join.
Then the game was over. I will certainly try again on normal (I lost a few times on normal before I decided to go on easy).