This can be done much easier: In memory pre-last During the last assassination mission, where you need to kill Robert in Jerusalem.
When your cover will be blown run away from the graveyard and try to continue the chase through the streets so that you can attract the attentions of the vast numbers of guards. Then make it to the rooftops and continue you rabid run from them.
You can occasionally stop and engage into fight to complete the "Eagle's Challenge" achievement. You can kill 5 of them for example then run for couple of minutes then kill other 10 - again running and so on. Kills counts towards the achievement while your HUD is in Red state.
The point is that while you're chased by "Robert" you cannot break the line of sight even if you are far away from him. That is why this two achievements "Eagle's Flight & Challenge" are easy to be done during this mission.