As many people will have found out, the "dictionary hints" provided by Duolingo are woefully inadequate. Here are some suggestions for better dictionaries. I've included several links for Portuguese and a couple for English (for learners using English as an intermediate language). The list includes some traditional style PT-EN translating dictionaries (like the first two entries), some optimized for online use in various ways, and others depend on your ability to read some Portuguese to be useful, although it's surprising how much you can glean from them with even the barest minimum of Portuguese knowledge.
Collins http://dictionary.reverso.net/portuguese-english/ I like this one because it has short pithy entries and it is easy to copy-paste an entry into a discussion like this: http://dictionary.reverso.net/portuguese-english/gostar. There are also several translating dictionaries for other languages if you start from http://dictionary.reverso.net/. A recently added feature is a translation database which is automatically searched whenever you consult the dictionary. It can be used separately via: http://context.reverso.net/translation/portuguese-english. (See this discussion for a cautionary tale: https://www.duolingo.com/comment/13260610).
Michaelis http://michaelis.uol.com.br/ A set of Brazilian dictionaries. There is a Portuguese only dictionary and several translating dictionaries: two for English and ones for Spanish, German, French and Italian. The English entries are more extensive than in the Collins although sometimes the English used in the definitions is a bit quirky.
Pons http://en.pons.eu/ Another translating dictionary and although entries are quite basic it has the unique feature that you can hear many Portuguese words spoken with either a European or Brazilian accent depending on your choice.
Priberam http://www.priberam.pt/dlpo/ The nice thing about this dictionary from Portugal is that it highlights differences between Brazilian Portuguese and European Portuguese spelling. If you own a recent Kindle (or use one of the Kindle apps) then this is the dictionary that is loaded up when you read a Portuguese language book.
Infopedia http://www.infopedia.pt/ A second online dictionary (and encyclopedia) from Portugal. Includes many useful tools found using the hover-over menus above the search box. Worth trying!
Aulete http://www.aulete.com.br/ This is a single language Portuguese dictionary with an enormous number of entries. Good for obscure words.
Houaiss http://dicionario.cijun.sp.gov.br/houaiss/ One of the two major dictionaries sold in Brazil (along with the Aurélio) Even though this version is a little bit out of date, this is a really useful single language dictionary. A major problem, however, is that it does not render correctly in some browsers. I have to manually change the page settings to get it to work. (I suspect this link is not meant to be accessed by the public).
Aurélio http://www.dicionariodoaurelio.com/ A best seller in Brazil. Unfortunately there isn't a site that gives free access to the full single language dictionary - this seems to be a slightly watered down version and I don't think the entries are really taken from the current Aurélio.
Dicionário Online http://www.dicio.com.br/ Another single language dictionary. Two useful features of this one are that it often gives examples from contemporary sources and it also includes conjugation information for verbs (or if conjugation of verbs is all you want there is an associated site here: http://www.conjugacao.com.br/).
Dicionário Informal http://www.dicionarioinformal.com.br/ A dictionary where the entries are defined by its users. The first place to look for slang.
Vocabulário Ortográfico da Língua Portuguesa http://www.academia.org.br/abl/cgi/cgilua.exe/sys/start.htm?sid=23 A list compiled by the Academia Brasileira de Letras of the 381,000 words in the Portuguese Language (no definitions are provided so it is not really a dictionary).
FLiP Corrector ortográfico e sintáctico
http://www.flip.pt/FLiP-On-line/Corrector-ortografico-e-sintactico.aspx Spelling and grammar checker.
Portal da Língua Portuguesa http://www.portaldalinguaportuguesa.org/main.html A collection of very useful tools including a crossword dictionary and a list of phonetic transcriptions of many words.
Linguee http://www.linguee.com/ This is a dictionary like no other. You enter a word or phrase and it searches a corpus of documents that are available in both Portuguese and English and shows them side-by-side. You can see how the language works this way.
Free Dictionary http://www.thefreedictionary.com/ Claims to be the world's most comprehensive dictionary. Excellent English section and several more dictionaries in other languages (recommended by native Portuguese speaker erudis).
WordReference http://www.wordreference.com/pten/ Similar in style to the Free Dictionary, short definitions with example sentences.
Oxford http://oxforddictionaries.com/ This is an English dictionary with separate sections for British and US English. The site includes several translating dictionaries too. See also: http://www.oxfordlearnersdictionaries.com/
Cambridge http://dictionary.cambridge.org/dictionary/english-portuguese/ An English to Portuguese dictionary which is helpful in finding the nearest Portuguese equivalents for English phrasal verbs.
Longman http://www.ldoceonline.com Another English dictionary with comprehensive definitions and one that's become a favourite of mine.
Merriam-Webster http://www.merriam-webster.com/ A good US English dictionary. Often more complete than the US English section of the Oxford. Even better is their learner's dictionary: http://www.learnersdictionary.com
Conjuga-me http://www.conjuga-me.net/ Although not a dictionary, this is an incredibly useful site. Enter any verb and it produces a table of conjugations. What's even better is that it highlights irregular entries in red. It is also easy to copy-paste entries into discussions like this: http://www.conjuga-me.net/verbo-perder - brilliant.
Want even more? http://www.lexilogos.com/english/portuguese_dictionary.htm Try this or the English dictionary agregator http://www.onelook.com
NOTE Portuguese spelling has changed over time and even though a spelling reform came into force in January 2009 there are still differences between Brazilian and European Portuguese. These differences go further than spelling and the lexicon itself is different:
If you don't know whether the translating dictionary you are using is Brazilian or not, or pre-reform or not, try looking up the Portuguese word "comboio" and the English word "idea". If "comboio" is translated as "convoy" or as "train (PT)" or if "train" is one of the last definitions, then it's likely to be Brazilian. If "idea" is translated as "idéia" (with an acute accent) then it's likely to be using pre-2009 spelling.
I hope this helps you.
It would be great if DL made it easy to save for reference great posts like this. There is so much to learn from the comments, but DL provides no way that I know of to keep track of and easily references great posts. Alas, I have been using Evernote as an alternative to track them. It's working well enough, but not as well as it would if DL added such functionality natively (am I misspelling this word? My spell checker is marking it wrong, but with no correct alternative offered.).
One thing you might want to add for https://www.linguee.com: all audio examples are read by a Brazilian and a Portuguese native speaker.
Of your other resources I found only Collins/Reverso and Pons having audio examples but in German (because I'm a German native speaker) there are examples where you can hear they are computer-generated and I expect it to be no different in Portuguese (ex. https://en.pons.com/translate?l=deen&q=Trottoir and https://dictionary.reverso.net/german-english/Hagestolz). Another indicator is that they have audio for every word no matter how rare, where in Linguee there simply is no audio for rare words.