The guardian article seems to more or less include the data that's in the WWF report.
Similar data is reported in the literature. For instance, this article  from Science says
Our analyses suggest that biodiversity has continued to decline over the past four decades, with most (8 out of 10) state indicators showing negative trends (Fig. 1 and Table 1). There have been declines in population trends of (i) vertebrates (13) and (ii) habitat specialist birds; (iii) shorebird populations worldwide; extent of (iv) forest (14, 15); (v) mangroves; (vi) seagrass beds; and (vii) the condition of coral reefs. None show significant recent reductions in the rate of decline (Table 1), which is either fluctuating (i), stable (ii), based on too few data to test significance (iii to vi), or stable after a deceleration two decades ago (vii). Two indicators, freshwater quality and trophic integrity in the marine ecosystem, show stable and marginally improving trends, respectively, which are likely explained by geographic biases in data availability for the former and spatial expansion of fisheries for the latter (5). Aggregated trends across state indicators have declined, with no significant recent reduction in rate: The most recent inflection in the index (in 1972) was negative (Fig. 2). Because there were fewer indicators with trend data in the 1970s, we recalculated the index from 1980, which also showed accelerating biodiversity loss: The most recent inflection (2004) was negative. Finally, aggregated species’ extinction risk (i.e., biodiversity loss at the species level) has accelerated: The International Union for Conservation of Nature (IUCN) Red List Index (RLI), measuring rate of change (16, 17), shows negative trends.
The article mentions some specific data in the referenced table. Key points (data for 1970-2010):
mean population trends of vertebrates: -31%
Wild Bird Index: mean population trends of habitat specialists in Europe and North America: -2.6%
shorebird populations: -33%
If you are concerned about the methods used to generate the data in the WWF report, see . This covers how data is collected, what data is collected, how data is aggregated, limitations in the data set, population aggregates and divisions. The paper also discusses trends and analysis. As an example, you'll find discussion like the following in the paper:
These issues highlight concerns over indicators of biodiversity change that are more wide reaching. The factor that most limits progress in understanding biodiversity change is that many of the existing data relate to species from temperate regions, whereas the majority of biodiversity is found in the tropics.
In summary, it's not clear to me where the 60% number came from in the original question. But the "big picture" being reported is approximately correct, and the numbers are more or less worse than 60% depending on what populations you consider.
 Global Biodiversity: Indicators of Recent Declines, Science 28 May 2010: Vol. 328, Issue 5982, pp. 1164-1168. DOI: 10.1126/science.1187512
 Monitoring Change in Vertebrate Abundance: the Living Planet Index, Conservation Biology, 23: 317-327. doi:10.1111/j.1523-1739.2008.01117.x