Do A LOT of side quests. Don't worry if you get one ally first and later the other. You can get two per playthrough only. It is possible to get these achievements even before going to Ilos if you complete every possible side quest and all main missions.
Basic plan of attack for ally achievements:
* Complete Eden Prime
* Go to Citadel, talk to Council
* Find Harkin (Chora's Den), Garrus (Med Clinic) and Wrex (C-Sec)
* Take care of Fist (do not pick up his OSD!)
* Rescue Tali in the Wards Access
* Talk to Council, become Spectre
* Head to Therum and rescue Liara
From here, you will have all the allies. Pick the two you want to use and use them for EVERYTHING. If you don't have an ally with decryption and need them to unlock a quest by hacking a computer, switch them in to receive the quest, then immediately go back and switch them out.
Now with your two allies:
* Complete any possible Citadel assignment
* Complete any random space assignments
* Complete Noveria (do all assignments BEFORE leaving the arrival site)
* Complete Feros (do all assignments BEFORE leaving the arrival site)
* Go back to the Citadel and complete any assignments you started on Noveria/Feros
* Complete Virmire (do not kill Wrex!)
* Back to the Citadel once more
You should have the achievements by now, but if you don't, head to Ilos and finish out the game. Many people got a few of the achievements (mainly Liara) at the very last mission.