I wouldn't say Moyes has over-achieved every season, he did amazingly well to get to the CL qualifying phase, but qualifying for the Europa or thereabouts isn't really that amazing.
As pointed out before, Allardyce has a comparable record, do we consider him too?
Look at the wage table, and then look at where Everton have finsihed under Moyes, and look where he's taken them from where they were before he arrived.
1999-2k 38 7 9 3 36 19 5 5 9 23 28 +12 50 13th
2000-01 38 6 8 5 29 27 5 1 13 16 32 -14 42 16th
2001-02 38 8 4 7 26 23 3 6 10 19 34 -12 43 15th
2002-03 38 11 5 3 28 19 6 3 10 20 30 -1 59 7th
2003-04 38 8 5 6 27 20 1 7 11 18 37 -12 39 17th
2004-05 38 12 2 5 24 15 6 5 8 21 31 -1 61 4th
2005-06 38 8 4 7 22 22 6 4 9 12 27 -15 50 11th
2006-07 38 11 4 4 33 17 4 9 6 19 19 +16 58 6th
2007-08 38 11 4 4 34 17 8 4 7 21 16 +22 65 5th
2008-09 38 8 6 5 31 20 9 6 4 24 17 +18 63 5th
2009-10 38 11 6 2 35 21 5 7 7 25 28 +11 61 8th
Add to this the fact he has spent next to no money and I think its fair to say he has overachieved in every season with the possible exception of 05-06.